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.
