Two intersecting curves are graphed on a coordinate plane.

Question

The dotted graph is a reflection of the solid graph. The solid graph is a cubic function with the equation f(x)=x3+1
. Enter the option number that shows the equation of the image.

Option #1: g(x)=−x2+1


Option #2: g(x)=−x3−1


Option #3: g(x)=−x3+1


Option #4: g(x)=x3−1

Answer 1

The image of the cubic function through reflection will have the same magnitude but opposite sign.

Therefore, the equation of the image will be g(x) = -x^3 + 1.

So, the correct option is #3: g(x) = -x^3 + 1.