Question

4. The original function is f(x) = x². Circle the type of reflection that has occurred (x-axis, y-axis or neither). a. g(x) = -x² b. h(x) = 2/1/2x² c. k(x) = (-x)² x-axis x-axis x-axis y-axis y-axis y-axis neither neither neither ​

Answer 1

Explanation:

a. g(x) = -x² x-axis

what was originally above the x-axis (positive function values), is now below (negative function values). and vice versa.

b. h(x) = 1/2 x² neither

this does not flip things around. it only "squeezes" the curve down a little bit.

c. k(x) = (-x)² y-axis

although we would not notice. this turns negative x-values to positive ones, and positive x- values into negative ones. so, the left side of the curve trades place with the right side.

but because the left side of the original function is already the mirror image of the right side, we don't see a difference in the graph when mirroring the sides. but we did reflect across the y-axis.