Schneider Cox
03/19/2023 · Junior High School
Question 3 (1 poing Is the equation for the graph of \( f(x)=-x^{2}-5 \) reflected across the \( y \)-axis the same equation? True False
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Step-by-step Solution
To determine if the equation for the graph of \( f(x) = -x^2 - 5 \) reflected across the \( y \)-axis is the same, we need to find the equation of the reflected graph.
When a function is reflected across the \( y \)-axis, we replace \( x \) with \( -x \) in the function. Therefore, we have:
\[
f(-x) = -(-x)^2 - 5 = -x^2 - 5
\]
This shows that the reflected function \( f(-x) \) is:
\[
f(-x) = -x^2 - 5
\]
Since \( f(-x) = f(x) \), the equation for the graph of \( f(x) = -x^2 - 5 \) reflected across the \( y \)-axis is indeed the same equation.
Thus, the answer is **True**.
Quick Answer
The equation remains the same after reflection across the \( y \)-axis. True.
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