The dotted graph is a reflection of the solid graph. The solid graph is a cubic function with the equation f(x) = x 3 + 1. Which equation shows the image? (1 point) Responses g(x) = -x2 + 1 g(x) = -x2+ 1 g(x) = -x3 - 1 g(x) = -x 3 - 1 g(x) = -x3 + 1 g(x) = -x 3 + 1 g(x) = -x3 - 1

Answer 1

To find the reflection of the solid graph \(f(x) = x^3 + 1\), we should consider what reflection means in this context. Assuming that the reflection is across the x-axis, we would negate the output of the function.

Therefore, if we reflect \(f(x)\) across the x-axis, the new function \(g(x)\) can be found by taking the negative of \(f(x)\):

\[ g(x) = -f(x) = -(x^3 + 1) = -x^3 - 1 \]

Thus, the equation that shows the image of the reflection is:

g(x) = -x³ - 1.