dotted graph is a reflection of the solid graph. The solid graph is a cubic function with the equation f(x)=x^3+1 option number that shows the equation of the image. . Enter the Option #1: g(x)=-x^2+1 Option #2: g(x)=-x^3-1 Option #3: g(x)=-x^3+1 Option #4: g(x)=x^3-1 (1 point) The equation of the dotted graph is Option # □ .

Answer 1

To find the equation of the dotted graph, which is a reflection of the solid graph \( f(x) = x^3 + 1 \), we should determine how reflections work.

The reflection across the x-axis can be achieved by negating the output of the function.

Thus, if \( f(x) = x^3 + 1 \), the reflected function \( g(x) \) would be:

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

Now, let's look at the options provided:

• Option #1: \( g(x) = -x^2 + 1 \)
• Option #2: \( g(x) = -x^3 - 1 \)
• Option #3: \( g(x) = -x^3 + 1 \)
• Option #4: \( g(x) = x^3 - 1 \)

The correct option reflecting the equation of the dotted graph is:

Option #2: \( g(x) = -x^3 - 1 \).

Therefore, the answer is Option #2.