Exercise 172 Page 115

a When we multiply the input of a function by -1, the function's graph reflects in the y-axis. This means the x-coordinate of every point on the original graph changes sign but the y-coordinate stays the same.

|c|c| [-1em] (x,f(x)) & (- x,f(- x)) [0.2em] [-1em] (-6,-5) & (6,-5) [0.2em] [-1em] (-4,-3) & (4,-3) [0.2em] [-1em] (-2,-1) & (2,-1) [0.2em] [-1em] (0,-3) & (0,-3) [0.2em] [-1em] (2,-5) & (-2,-3) [0.2em] Let's mark these new points in a coordinate plane and show the transformation.

b Like in Part B, we have to reflect all points of the original graph in the y-axis.

|c|c| [-1em] (x,f(x)) & (- x,f(- x)) [0.2em] [-1em] (-4,1.75) & (4,1.75) [0.2em] [-1em] (-2,1.5) & (2,1.5) [0.2em] [-1em] (-0.5,0) & (0.5,0) [0.2em] [-1em] (-0.25,-2) & (0.25,2) [0.2em] [-1em] (0.25,6) & (-0.25,6) [0.2em] [-1em] (0.5,5) & (-0.5,5) [0.2em] [-1em] (2,2.5) & (-2,2.5) [0.2em] Let's mark these new points in a coordinate plane and show the transformation.

c Like in Parts A and B we will reflect all points that fall on the original graph in the y-axis.

|c|c| [-1em] (x,f(x)) & (- x,f(- x)) [0.2em] [-1em] (- 10,-2.2) & (10,- 2.2) [0.2em] [-1em] (-7,-2.5) & (7,-2.5) [0.2em] [-1em] (-5.5,-4) & (5.5,-4) [0.2em] [-1em] (-5.25,-6) & (5.25,-6) [0.2em] [-1em] (-4.75,2) & (4.75,2) [0.2em] [-1em] (-4.5,0) & (4.5,0) [0.2em] [-1em] (-3,-1.5) & (3,-1.5) [0.2em] [-1em] (0,-1.8) & (0,-1.8) [0.2em] Let's mark these new points in a coordinate plane and show the transformation.

d Like in previous parts, we will reflect all points that fall on the original graph in the y-axis.

|c|c| [-1em] (x,f(x)) & (- x,f(- x)) [0.2em] [-1em] (- 2,-13) & (2,- 13) [0.2em] [-1em] (-1,6) & (1,6) [0.2em] [-1em] (0,5) & (0,5) [0.2em] [-1em] (1,4) & (-1,4) [0.2em] [-1em] (2,-3) & (-2,-3) [0.2em] Let's mark these new points in a coordinate plane and show the transformation.

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Exercise 172 Page 115

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