Question
Use the image to answer the question.
Two intersecting curves are graphed on a coordinate plane.
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 #
.
Two intersecting curves are graphed on a coordinate plane.
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 #
.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the equation of the dotted graph, which is a reflection of the solid graph \( f(x) = x^3 + 1 \) across the x-axis, you need to negate the output of the function.
The reflection across the x-axis would mean that if \( f(x) = y \), then the reflected graph would be \( g(x) = -y \).
So, apply this to the equation:
1. Start with the original function:
\[
f(x) = x^3 + 1
\]
2. Reflect it across the x-axis:
\[
g(x) = -(x^3 + 1) = -x^3 - 1
\]
Thus, the equation of the dotted graph is \( g(x) = -x^3 - 1 \).
Therefore, the answer is Option #2.
The reflection across the x-axis would mean that if \( f(x) = y \), then the reflected graph would be \( g(x) = -y \).
So, apply this to the equation:
1. Start with the original function:
\[
f(x) = x^3 + 1
\]
2. Reflect it across the x-axis:
\[
g(x) = -(x^3 + 1) = -x^3 - 1
\]
Thus, the equation of the dotted graph is \( g(x) = -x^3 - 1 \).
Therefore, the answer is Option #2.
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