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


(1 point)
The equation of the dotted graph is Option #
.

Answer 1

To find the reflection of the solid graph represented by the function \( f(x) = x^3 + 1 \), we first note that a reflection across the x-axis involves negating the entire function.

Thus, the reflected function \( g(x) \) will be:

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

Now, looking at the provided options, we see that:

- Option #1: \( g(x) = -x^2 + 1 \) (not a cubic function)
- Option #2: \( g(x) = -x^3 - 1 \) (this is our equation)
- Option #3: \( g(x) = -x^3 + 1 \) (does not match)
- Option #4: \( g(x) = x^3 - 1 \) (does not match)

Therefore, the correct choice for the equation of the dotted graph is:

**Option #2**.