Question
What is the effect on the graph of f(x)=x3
when f(x)
is replaced by f(−x)
?(1 point)
Responses
the range changing to only negative values of y
the range changing to only negative values of y
the domain changing to only negative values of x
the domain changing to only negative values of x
a reflection about the line y=x
a reflection about the line y is equal to x
a reflection about the y-axis
a reflection about the y -axis
when f(x)
is replaced by f(−x)
?(1 point)
Responses
the range changing to only negative values of y
the range changing to only negative values of y
the domain changing to only negative values of x
the domain changing to only negative values of x
a reflection about the line y=x
a reflection about the line y is equal to x
a reflection about the y-axis
a reflection about the y -axis
Answers
GPT-4o mini
When \( f(x) = x^3 \) is replaced by \( f(-x) \), the new function becomes
\[
f(-x) = (-x)^3 = -x^3.
\]
This means that the graph of \( f(-x) \) is a reflection of the graph of \( f(x) \) about the y-axis.
Therefore, the correct response is:
**a reflection about the y-axis**.
\[
f(-x) = (-x)^3 = -x^3.
\]
This means that the graph of \( f(-x) \) is a reflection of the graph of \( f(x) \) about the y-axis.
Therefore, the correct response is:
**a reflection about the y-axis**.