To find the equation of the dotted graph, which is a reflection of the solid graph (the cubic function \( f(x) = x^3 + 1 \)), we need to determine the reflection across the x-axis.
The reflection of a function \( f(x) \) across the x-axis is given by \( g(x) = -f(x) \).
So, applying this to the given function:
- Start with \( f(x) = x^3 + 1 \).
- To reflect it, take the negative: \[ g(x) = -f(x) = -(x^3 + 1) = -x^3 - 1 \]
This matches with Option #2: \( g(x) = -x^3 - 1 \).
Therefore, the answer is:
Option #2.