Question

Given the graphed function f(x)=(x+3)^2-2 determine g(x) if it is a reflection of f(x) over the y axis.

G(x)=-(x+3)^2-2
G(x)=(-x+3)^2-2
G(x)=(-x-3)^2-2
G(x)=(-x+3)^2+2

Answer 1

Are you sure that's right

Answer 2

To find \( g(x) \), which is the reflection of \( f(x) = (x + 3)^2 - 2 \) over the y-axis, we replace \( x \) with \( -x \) in the function \( f(x) \).

Starting with the original function:

\[
f(x) = (x + 3)^2 - 2
\]

Now, replace \( x \) with \( -x \):

\[
g(x) = f(-x) = (-x + 3)^2 - 2
\]

This simplifies directly to:

\[
g(x) = (-x + 3)^2 - 2
\]

Thus, the expression for \( g(x) \) is:

\[
g(x) = (-x + 3)^2 - 2
\]

Among the given choices, the correct answer is:

\[
G(x) = (-x + 3)^2 - 2
\]

Answer 3

Let's confirm the reflection process to ensure the correct answer.

Given the function:
\[
f(x) = (x + 3)^2 - 2
\]

To find \( g(x) \), which is the reflection of \( f(x) \) over the y-axis, we need to replace \( x \) with \( -x \):

\[
g(x) = f(-x) = ((-x) + 3)^2 - 2
\]

This simplifies to:

\[
g(x) = (-x + 3)^2 - 2
\]

Thus, the expression for \( g(x) \) we found is indeed:

\[
g(x) = (-x + 3)^2 - 2
\]

This matches choice \( G(x) = (-x + 3)^2 - 2 \), confirming that the previous response was correct.

If there's any specific part you would like to clarify or further explore, please let me know!