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: 9 (x) = -x? + 1
Option #2:g （zc） =- ”- 1
Option #3: 9 (x) = -x3+1
Option #4: 9 (x) = x -1
(1 point)
equation f(x) = x3 + 1. Enter the
option number that shows the equation of the image.
Option #1: 9 (x) = -x? + 1
Option #2:g （zc） =- ”- 1
Option #3: 9 (x) = -x3+1
Option #4: 9 (x) = x -1
(1 point)
Answers
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Answered by
GPT-4o mini
To find the equation of the reflected cubic function based on the given solid graph \( f(x) = x^3 + 1 \), we need to consider the reflection.
The reflection of a function across the x-axis requires negating the function. Hence, the reflection of \( f(x) \) will be:
\[
g(x) = -f(x) = -(x^3 + 1) = -x^3 - 1
\]
Looking at the options provided:
1. Option #1: \( g(x) = -x^2 + 1 \)
2. Option #2: \( g(x) = -” - 1 \) (not a valid option)
3. Option #3: \( g(x) = -x^3 + 1 \)
4. Option #4: \( g(x) = x - 1 \)
None of the options perfectly match \( g(x) = -x^3 - 1 \), which is the correct reflection. However, option #3 \( g(x) = -x^3 + 1 \) is actually incorrect too but seems the closest in form if the constant sign was adjusted.
Since we do not have the exact reflection among the options, it looks like either there was a mistake in the options or the correct reflection wasn't included properly.
If I must choose an answer, I'd choose **Option #3 (g(x) = -x^3 + 1)** but please be aware that this would not be the actual reflection you've calculated.
The reflection of a function across the x-axis requires negating the function. Hence, the reflection of \( f(x) \) will be:
\[
g(x) = -f(x) = -(x^3 + 1) = -x^3 - 1
\]
Looking at the options provided:
1. Option #1: \( g(x) = -x^2 + 1 \)
2. Option #2: \( g(x) = -” - 1 \) (not a valid option)
3. Option #3: \( g(x) = -x^3 + 1 \)
4. Option #4: \( g(x) = x - 1 \)
None of the options perfectly match \( g(x) = -x^3 - 1 \), which is the correct reflection. However, option #3 \( g(x) = -x^3 + 1 \) is actually incorrect too but seems the closest in form if the constant sign was adjusted.
Since we do not have the exact reflection among the options, it looks like either there was a mistake in the options or the correct reflection wasn't included properly.
If I must choose an answer, I'd choose **Option #3 (g(x) = -x^3 + 1)** but please be aware that this would not be the actual reflection you've calculated.
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