Two intersecting curves are graphed on a coordinate plane.
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
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.