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MATH 107 Mathematics Equations & Functions Solved Quiz 3

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Name: ____________________ Date: _____________________ MATH 107 Quiz 3 1) Sketch the graph of the given piecewise-defined function. 2) Determine analytically if the following functions are even, odd or neither. y = x4 − 6x2 + 5 : If f (− x) = f (x) then the function is even. If f (− x) =− f (x) then the function is odd. Since y is f (x) . f (x) = x4 − 6x2 + 5 f (− x) = (− x)4 − 6(− x)2 + 5 4 2 f (− x) = (− 1)4 (x) − 6(− 1)2 (x) + 5 f (− x) = x4 − 6x2 + 5 Therefore, f (− x) = f (x) . This function is even. 3) Suppose (5, −4) is on the graph of y = f(x). Find a point on the graph of the given transformed functions. a. y = f (x − 4) + 1 x−4=5 x=9 So, y = f (x − 4) + 1 y = f (9 − 4) + 1 y = f (5) + 1 y =− 4 + 1 y =− 3 Final answer: (9,-3) b. y = 4f (2x) 2x = 5 x = 25 So, y = 4f (2x) y = 4f (2 * 25 ) y = 4f (5) y = 4 *− 4 y =− 16 Final answer: ( 25 ,− 16) c. y = 4−f (2x+1) 9 2x + 1 = 5; 2x = 4; x = 2 x=2 4−f (2x+1) 9 4−f (2(2)+1) 9 4−f (5) 9 4−(−4) 9 8 9 So, y = y= y= y= y= Final answer: (2, 98 ) 4) The complete graph of y = f(x) is given below. Sketch the given transformation function y = 3 − f (4 − 2x) . For (-2,2), 4 − 2x =− 2; − 2x =− 6; x = 3 y y y y y = 3 − f (4 − 2x) = 3 − f (4 − 2(3)) = 3 − f (− 2) =3−2 =1 For (0,0), 4 − 2x = 0; − 2x =− 4; x = 2 y y y y y = 3 − f (4 − 2x) = 3 − f (4 − 2(2)) = 3 − f (0) =3−0 =3 For (2,2), 4 − 2x = 2; − 2x =− 2; ...
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