A Graphical Approach to College Algebra (7th Edition)

Chapter 2

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 The original graph and the graph after rotating ... more

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The graph  is symmetric around the origin means i... more

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Squaring function ; The function is symmetric ... more

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Cubic function ; With respect to origin, the ... more

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Square root function ; The function is symmetric ... more

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A graph is symmetric with respect to x-axis means ... more

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; Check all the function wether odd , even or ... more

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real numbers ; Now, Identity function means so it ... more

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; Squaring function means Domian: All the values ... more

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; Cubing function means Draw the graph using the ... more

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; Square root function means Draw the graphing ... more

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increases ; Cube root function means Draw the ... more

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; Absolute value function means Draw the graph ... more

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x-axis ; Draw the graph of the relation On ... more

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even ; For a function to be even function For a ... more

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odd ; For a function to be odd For a function  ... more

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y-axis  ; For a  function to be even function ... more

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; On observing the graph the curve is taking ... more

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; On observing the graph the curve is taking ... more

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; On observing the graph the curve is taking only... more

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; The given graph can be drawn from to infinite ... more

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; The given graph is having vertical asymptote at... more

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; The given graph is discontinuous at point . ... more

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Over the specified interval of ; as one moves from... more

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The y-value decreases as one moves from left to ... more

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The function value decreases which means the y-... more

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The function increases which means the y-value ... more

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The function is increasing which means the y-value... more

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The y-value decreases as one moves from left to ... more

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The function increases which means the y-value ... more

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Decreasing ; To graph the function in the graphing... more

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Decreasing ; To graph the function in the graphing... more

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Increasing ; To graph the function in the graphing... more

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Increasing ; To graph the function in the graphing... more

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Decreasing ; To graph the function in the graphing... more

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Function is called even function if . ; Function... more

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It is observed that for odd functions,   for all ... more

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x-3-2-1123f(x)21-12-25-25-1221 ; Function is ... more

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x-5-3-20235g(x)131-505-1-13 ; Function is called ... more

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Even ; Function is called even if and function ... more

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Even ; Function is called even if and function ... more

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Odd ; Function is called even if and function ... more

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Odd ; Function is called even if and function ... more

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Neither even nor odd ; Function is said to be a ... more

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Neither even nor odd ; Function is said to be a ... more

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, even function ; Replace with in the function ... more

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, even function ; Replace with in the function ... more

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, odd function ; Replace with in the function ... more

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, odd function ; Replace with in the function ... more

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, even function ; Replace with in the function ... more

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, even function ; Replace with in the function ... more

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, odd function ; Replace with in the function ... more

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, odd function ; Replace with in the function ... more

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, even function ; Replace with in the function ... more

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, even function ; Replace with in the function ... more

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, odd function ; Replace with in the function ... more

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, odd function ; Replace with in the function ... more

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, even function ; Replace with in the function ... more

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, odd function ; Replace with in the function ... more

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, odd function ; Replace with in the function ... more

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, odd function ; Replace with in the function ... more

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, even function ; Replace with in the function ... more

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, even function ; Replace with in the function ... more

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The function is symmetric to the origin. ; There ... more

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The function is symmetric to the origin. ; There ... more

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The function is symmetric to -axis. ; There are ... more

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The function is symmetric to -axis. ; There are ... more

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The function is neither symmetric to origin nor -... more

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The function is neither symmetric to origin nor -... more

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The function is neither symmetric to origin nor -... more

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The function is symmetric to the origin. ; There ... more

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The function is symmetric with respect to -axis... more

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The function is symmetric with respect to -axis... more

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The function is symmetric to the origin. ; There ... more

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The function is symmetric to the origin. ; First ... more

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From the graph of all the groups, it can be ... more

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The graph of is shifted upward with the distance ... more

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The graph of is shifted downward with the ... more

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With respect to , the graph of and is shifted to... more

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With respect to the graph of , the graph of is ... more

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With respect to the graph of , the graph of is ... more

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; When the graph of the function is shifted ... more

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; When the graph of the function is shifted ... more

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; In the expression, 4 units are shifted ... more

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; In the expression, 6 units are shifted upwards ... more

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; In the expression, 4 units are shifted to the ... more

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; In the expression, 3 units are shifted to the ... more

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; In the expression, 7 units are shifted to the ... more

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; In the expression, 9 units are shifted to the ... more

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; In the expression, 2 units are shifted ... more

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;  In the expression, 4 units are shifted upwards... more

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;  In the expression, 3 units are shifted upwards... more

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;  In the expression, 1 unit is shifted downwards... more

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;  In the expression, 500 units are shifted ... more

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; In the expression, 255 units are shifted ... more

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Shift the graph of upwards by 4 units to get the ... more

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Shift the graph of 4 units to the left, to get ... more

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The graph of is shifted 3 units downwards. ; The ... more

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The graph of is shifted 4 units upwards. ; The ... more

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The graph of is shifted 3 units to the right. ; ... more

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4 ; From the table, for , . ; more

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-2 ; From the table, for , . ; more

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1.5 ; From the table, for , . ; more

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-3 ; To solve follow these stepsA vertical shift ... more

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5 ; To solve follow these stepsA vertical shift ... more

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; The function is a quadratic functionThe value... more

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; The function is a quadratic functionThe value... more

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; The function is a square root functionThe ... more

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; The function is a square root functionThe ... more

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; The function is a cubic functionThe value is ... more

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; The function is a cubic functionThe value is ... more

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 Given function basic form is . So firsty draw the... more

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Given function basic form is . So first draw the ... more

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Given function basic form is . So first draw the ... more

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Given function basic form is . So first draw the ... more

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Given function basic form is . So first draw the ... more

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Given function basic form is . So first draw the ... more

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Given function basic form is . So first draw the ... more

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Given function basic form is . So first draw the ... more

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Given function basic form is . So first draw the ... more

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Given function basic form is . So first draw the ... more

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Given function basic form is . So first draw the ... more

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Given function basic form is . So first draw the ... more

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Given function basic form is . So first draw the ... more

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Given graph consists three different lines, so ... more

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Given graph consists three different lines, so ... more

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Given graph consists three different lines, so ... more

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Given graph consists three different lines, so ... more

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h=-3, k=1 ; Basic graph equation was y=|x|.  the ... more

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h=0, k=38 ; Basic graph was y=x^2, then graph was ... more

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31,474,883 dollars ; According to the given ,U(x)=... more

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Interpretation From the graph also it is observed ... more

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2 ; To subtract the numbers , first change the ... more

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; From exercise 78 , Adding 3 both sides ,  ; more

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; Find absolute values Do the subtraction with ... more

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; From exercise 81 , Adding 4 both sides The ... more

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c ; c ; the same as  ; c ; The line with new ... more

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The graphs of are vertical stretching of graph... more

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The graph of stretches vertically upwards . ; ... more

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When , the graph of   shrinks horizontally when ... more

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When y2 is compared with y1 graphs they are ... more

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It is noted from the graph that the is the graph ... more

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It is found that the graphs are reflected in y-... more

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When the graph of the function is compared with ... more

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The answer is . ; If , then the graph of is the ... more

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The answer is . ; If , then the graph of is the ... more

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The answer is . ; The function graph is the graph... more

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The answer is . ; The function graph is the graph... more

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The answer is . ; If , the graph of is the graph ... more

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The answer is . ; If , the graph of is the graph ... more

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The answer is . ; If , the graph of is the graph ... more

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The answer is . ; If , then the graph of is the ... more

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The answers are, ; It is clear that is a line ... more

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The answers are, ; It is clear that is a curve ... more

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The answers are, ; It is clear that  is the graph... more

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The answers are, ; It is clear that is the graph ... more

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The answers are, ; It is clear that is a curve ... more

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The answers are, ; It is clear that  is the graph... more

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The answers are, ; It is clear that is a curve ... more

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 Follow the steps below to draw  Insert values of... more

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Follow the steps below to draw . Insert values of... more

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Follow the steps below to draw Insert values of , ... more

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Follow the steps below to draw  Insert values of... more

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Follow the steps below to draw  Insert values of... more

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Follow the steps below to draw  Insert values of... more

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Follow the steps below to draw  Insert values of... more

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; Vertex is given as (5,-2). This implies that ... more

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; Vertex of transformed graph is (4,3). Therefore... more

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; Transformed graph is obtained by reflecting ... more

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; Transformed graph is obtained by reflecting ... more

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4 ; Factor 4 which is multiplied with term ... more

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6 ; Factor 6 multiplied with indicates vertical ... more

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2 ; Since coordinate is converted as in the ... more

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; Function is obtained by reflecting original ... more

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3 ; Since coordinate is converted as in the ... more

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2 ; Since coordinate is converted as in the ... more

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; Multiply with , since is shrunk by applying ... more

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; Multiply by a factor of 3, since is stretched ... more

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; Since, there is horizontal shift of 3 units to ... more

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; Start by shifting the graph of by 2 units to ... more

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Identify how many units function shifted right, ... more

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Identify how many units function shifted right, ... more

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Identify how many units function shifted right, ... more

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Identify how many units function shifted right, ... more

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Identify how many units function shifted or ... more

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Identify how many units function shifted or ... more

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Identify how many units function shifted or ... more

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Identify how many units function shifted or ... more

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Identify how many units function shifted or ... more

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Identify how many units function shifted right, ... more

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Identify how many units function shifted right, ... more

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Identify how many units function shifted right, ... more

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Identify how many units function shifted right, ... more

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Identify how many units function shifted right, ... more

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Identify how many units function shifted right, ... more

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Identify how many units function shifted right, ... more

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Identify how many units function shifted right, ... more

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Identify how many units function shifted right, ... more

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Identify how many units function shifted right, ... more

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Find root of the equation. ; After getting the ... more

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domain:[1,4]range:[-2,1] ; the domain of has ... more

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domain:[-1.2,-0.6]range:[1,16] ; the domain of ... more

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domain:range: ; the domain of has given and ... more

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domain:;range:  ; the domain of has given \[-1,2... more

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domain:[-0.5,1]range:[0,6]  ; the domain of has ... more

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domain:[0.5,2]range:[-2,4]  ; the domain of has ... more

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domain:range:  ; the domain of has given and ... more

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domain:range:  ; the domain of has given and ... more

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domain:range:  ; the domain of has given and ... more

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domain:range:  ; the domain of has given and ... more

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domain:range:  ; the domain of has given and ... more

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domain:[6,15]range:[-1,0]  ; the domain of has ... more

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domain:[20,undefined)range:[5,undefined) ; The ... more

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domain:[-15,undefined)range:(-undefined,-18]  ; A ... more

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domain:[-10,undefined)range:(-undefined,5]  ; A ... more

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domain:[1,undefined)range:[1,undefined)  ; A ... more

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The graph of - is the reflection of graph across ... more

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The graph of is the reflection of the graph ... more

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The graph of is the reflection of the graph ... more

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The graph of is the reflection of the graph ... more

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The co-ordinates of the point on the graph of is... more

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The co-ordinates of the point on the graph of is... more

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The equation of the graph is 2 - 1. ; The lowest ... more

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The equation of the graph is = - + 2. ; The ... more

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In the given graph ,the shift is in upward ... more

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y=|x|+2 ; In the given graph ,the shift is in the ... more

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y=|x|-4 ; In the given graph ,the shift is in the ... more

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3y=-|x+3|+15 ; In the given graph ,the shift is in... more

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A function is symmetric about "y" axis implies f(x... more

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No ; A function is symmetric about "y" axis ... more

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This is an equation of parabola symmetric to y ... more

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This is an equation of parabola symmetric to y ... more

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The graphs of and are identical along the path .... more

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The given equation is ; more

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The given inequality is Solving  The solution set ... more

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The given inequality is  Solving  The solution set... more

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Domain of both the functions is . Range of the ... more

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Domain of both the functions is . Range of the ... more

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Domain of both the functions is . Range of the ... more

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Domain of both the functions is . Range of the ... more

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Domain of both the functions is . Range of the ... more

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Domain of both the functions is . Range of the ... more

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Domain of both the functions is . Range of the ... more

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Domain of both the functions is . Range of the ... more

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Domain of both the functions is . Range of the ... more

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5 ; The value of any number comes outside from the... more

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Both graphs are same as a squared number is never ... more

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; The values of the modulus function is  always ... more

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; The Modulus of the every function is always ... more

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; The modulus  value of any function is always ... more

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The value of any modulus function is always gives ... more

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Domain of the Range of the Domain of Range of   ; ... more

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Domain of the Range of the Domain of Range of   ; ... more

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Domain of the Range of the Domain of Range of   ; ... more

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Domain of the Range of the Domain of Range of   ; ... more

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Graph (a) is obtained by considering the mirror ... more

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Consider the table for . x -3 -1 0y -1 1 2 ... more

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Consider the table for .x-401y-134 Consider the ... more

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Consider the table for . x12-1y-1-20Consider the ... more

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Consider the table for .x124y21-1Consider the ... more

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Consider the table for .x12-1y0.51-0.5Consider the... more

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Consider the table for .x12-1y-2-42Consider the ... more

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Consider the table for .x12-1y35-1 Consider the ... more

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Consider the table for .x0-1-2y30-3Consider the ... more

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Consider the table for .x01-2y-4-60 Consider the ... more

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Consider the table for .x01-2y-2-54 Consider the ... more

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Consider the table for .x120y-50-10 Consider the ... more

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Consider the table for .x01-1y4-412Consider the ... more

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The V-shaped graph is y=f(x). Absolute valued ... more

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The line graph shows for y=g(x).The graph is ... more

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; Absolute values functions will have two values ... more

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; Solve  the inequality for x and take the ... more

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; Solve the values of x by removing the modulus ... more

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; Remove the modulus symbol and simplify for the ... more

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{-6,2} ; Isolate the function of absolute value by... more

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. ; Isolate the absolute value function by adding ... more

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{-7, 1} ; Isolate the absolute value function by ... more

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; Isolate the absolute value function by ... more

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; Isolate the absolute value function by ... more

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{0,1} ; Isolate the absolute value function by ... more

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; Remove the absolute value function to obtain ... more

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; Remove the absolute value function to obtain ... more

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; Remove the absolute value function to obtain ... more

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; Remove the absolute value function to obtain ... more

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; Remove the absolute value function to obtain ... more

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; Remove the absolute value function to obtain ... more

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; Remove the absolute value function to obtain ... more

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x changes to <. ;   ; The solution is x< 18. ; more

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; Remove the absolute value function to obtain ... more

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The absolute value functions are always positive. ... more

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The inequality is not true. ; Functions of ... more

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The inequality is always true for all real values ... more

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The equation can be solved by removing the ... more

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Let solving is same as solving Therefore solution... more

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Let solving is same as solving Therefore solution... more

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Let solving is same as solving Therefore solution... more

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Let solving is same as solving Therefore solution... more

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; Error tolerance means the absolute difference ... more

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The graph sheet is taken and , are drawn. Lets ... more

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The graph sheet is taken and , are drawn. Lets ... more

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The graph is taken and axis are drawn. Lets and... more

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The graph is taken and axis are drawn. Lets and... more

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The graph is taken and axis are drawn. Lets and... more

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The graph is taken and axis are drawn. Lets and... more

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 The inequality for the weight is of the case 3 ... more

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  ; The variable ranges from 680 to 780. This can... more

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Case 1: Case 2: ; For the first case, the variable... more

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The price of the postal service is generally ... more

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The function has the value of in the interval of... more

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The function has the value of in the interval of... more

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The function has the value of in the interval of... more

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The function has the value of in the interval of... more

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The function has the value of in the interval of... more

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The function has the value of in the interval of... more

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The function has the value of in the interval of... more

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The function has the value of in the interval of... more

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The function has the value of in the interval of... more

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The function has the value of in the interval of... more

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The function has the value of in the interval of... more

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The function has the value of in the interval of... more

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The graph is linear for and quadratic for . ; The... more

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To graph the given piecewise function using ... more

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To graph the given piecewise function using ... more

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To graph the given piecewise function using ... more

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To graph the given piecewise function using ... more

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To graph the given piecewise function using ... more

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To graph the given piecewise function using ... more

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To graph the given piecewise function using ... more

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To graph the given piecewise function using ... more

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; {-1, 2} ; The graph of is consists of two parts... more

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; {-1, 1} ; The graph of is consists of two parts... more

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; ; The graph of is consists of two parts. One ... more

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; ; The graph of is consists of two parts. One ... more

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; ; The graph of is consists of two parts. One ... more

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; ; The graph of is consists of two parts. One ... more

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Because there are two different definitions of the... more

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doesn't have a unique value. ; For , there are ... more

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The graph of is obtained by the vertical shifting... more

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The graph of can be obtained by the reflection of... more

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The graph of can be obtained by the reflection of... more

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The graph of can be obtained by the horizontal ... more

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Create the graph of step up function ; Since the ... more

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Simply create the graph of the step up function or... more

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Create the graph of step up fucntion and invert ... more

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From the function of [x] deviate every bit by 2 ... more

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For minutes (0,3) the slope of the graph is 5 and ... more

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$ 1.25 ; The 1st  minute costs=  $  0.50The 2nd ... more

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The function for this graph can be obtained from ... more

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The person leaves at 40 mph to the place 20 miles ... more

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The rate is 5 gallons per minutes, therefore, ... more

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f(x)=x2     g(x)=2x-5(f+g)x= f(x)+g(x)(f+g)x= x2+... more

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40 ; f(x)=x2+3xg(x)=2x-1 ; more

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-5 ; We need to find so at firstwe should compute... more

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; We need to find , so we need to substitute in ... more

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; To find , we need to substitute f(x) in terms ... more

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23 ; For finding , we need to find f(3) and g(3) ... more

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-1 ; To find , we need to find f(-5) and g(-5) ; more

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196 ; for (fg)(4) we need to find f(4) and g(4) ; more

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0 ; for (fg)(-3) we need to find f(-3) and g(-3... more

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; for we need to find f(-1) and g(-1) ; more

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4 ; for we need to find f(4) and g(4) ;   ; more

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7 ; for we need to find f(2) and g(2) ; more

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3 ; for we need to find f(-2) and g(-2) ; more

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-3 ; for we need to find f(-2) and g(-2... more

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Undefined ; for we need to find and   ; here  , ... more

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Undefined ; for we need to find f(0) and g(0... more

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Domain of is .Domain of is .Domain of is . ; ... more

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; All these for -2All these for 0All these for ... more

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x-2024-2790-6910-8-8200-2-8 ; First subtract the ... more

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4 ; Since , it is given that so 3 will be mapped ... more

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The answer is 7 and 0. ; Here , substitute for x ... more

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The answer is -3. ; To find the composition ... more

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The answer is 3. ; To find the composition ... more

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The answer is 93. ; To find the composition ... more

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The answer is 123. ; To find the composition ... more

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Only one ; Let here is any constent, then ... more

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; First let's start with definition of ... more

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First let's start with definition of composition ... more

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First let's start with definition of composition ... more

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First let's start with definition of composition ... more

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First let's start with definition of composition ... more

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Identify how many units function shifted right, ... more

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The graph of can be drawn by the reflecting graph... more

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4 ; Follow below steps to calculate difference ... more

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5 ; Follow below steps to calculate difference ... more

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; The Difference quotient of the function is ; ... more

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; Difference function quotient. is ; Get   for... more

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; Difference function quotient. is ; Get   for... more

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; Difference function quotient is ; Get   for... more

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; Difference function quotient is ; Get   for... more

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; Write  as . ; more

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; Given function   . ; To check satisfies ; more

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The given function is Find any three points and ... more

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The given function is Find any three points and ... more

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The given function is  Find any three points and ... more

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The given function is  Find any three points and ... more

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The given function is  Find any three points and ... more

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The given function is  Find any three points and ... more

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The given function is  Find any three points and ... more

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The given function is  Find any three points and ... more

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The given function is  Find any three points and ... more

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The given function is  Find any three points and ... more

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The given function is  Find any three points and ... more

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The given function is  Find any three points and ... more

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and ; First express the given equation in the form... more

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 Symmetric with respect to both x-axis and y-axis... more

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A function is an even function when which means ... more

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(-6, 1) ; The inequality can be rewritten as or... more

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(2, 10) ; The inequality can be rewritten as or... more

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0 ; Find the values of and substitute in the ... more

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3 ; Find the values of and and substitute in the... more

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2 ; Find out the values of and and substitute in... more

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8 ; Find the values of and and substitute in the... more

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0 ; Find the values of and and substitute in the... more

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Undefined ; Find the values of and and ... more

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The domain has interval of and the correct option... more

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