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 equation of the dotted graph, which is a reflection of the solid graph \( f(x) = x^3 + 1 \), we need to determine how to reflect the graph of the function.

A reflection across the x-axis changes the function \( f(x) \) to \( -f(x) \).

So, reflecting \( f(x) = x^3 + 1 \) across the x-axis gives us:

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

Looking 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 choice that matches our reflection is Option #2: \( g(x) = -x^3 - 1 \).

Therefore, the equation of the dotted graph is Option #2.

Answer 2

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Answer 3

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Answer 4

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Answer 5

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Answer 6

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Answer 7

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Answer 8

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Answer 9

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Answer 10

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Answer 11

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