Question
What is the reflection of the function f(x) = x^2 + 2x over the y-axis?
Answers
GPT-4o mini
To find the reflection of the function \( f(x) = x^2 + 2x \) over the y-axis, we need to substitute \( -x \) for \( x \) in the function. This is because the reflection of a function over the y-axis involves taking the negative of the input.
So, we calculate \( f(-x) \):
\[
f(-x) = (-x)^2 + 2(-x)
\]
Calculating this step by step:
1. \((-x)^2 = x^2\)
2. \(2(-x) = -2x\)
Now combine these results:
\[
f(-x) = x^2 - 2x
\]
Thus, the reflection of the function \( f(x) = x^2 + 2x \) over the y-axis is:
\[
f(-x) = x^2 - 2x
\]
So, we calculate \( f(-x) \):
\[
f(-x) = (-x)^2 + 2(-x)
\]
Calculating this step by step:
1. \((-x)^2 = x^2\)
2. \(2(-x) = -2x\)
Now combine these results:
\[
f(-x) = x^2 - 2x
\]
Thus, the reflection of the function \( f(x) = x^2 + 2x \) over the y-axis is:
\[
f(-x) = x^2 - 2x
\]