Find g(x), where g(x) is the reflection across the y-axis of f(x)=–2x–8.g(x)=2x+8g(x)=2x–8g(x)=–2x–8g(x)=–2x+8Submit

To find $g(x)$, the reflection across the y-axis of the function $f(x) = -2x - 8$, we can follow these steps:

1. Break Down the Problem

We need to find the reflection of the given function $f(x)$ across the y-axis. For a function $f(x)$, its reflection across the y-axis is $g(x) = f(-x)$.

2. Relevant Concepts

The reflection across the y-axis involves replacing $x$ with $-x$ in the original function. Therefore, if $f(x) = -2x - 8$, then:

$g(x) = f(-x)$

3. Analysis and Detail

Now we will replace $x$ in the equation $f(x)$ with $-x$:

$g(x) = f(-x) = -2(-x) - 8$ $g(x) = 2x - 8$

4. Verify and Summarize

Having calculated $g(x)$, we can summarize:

• The original function is $f(x) = -2x - 8$.
• The reflection across the y-axis gives us $g(x) = 2x - 8$.

Final Answer

Therefore, the reflection $g(x)$ is: $g(x) = 2x - 8$