Questions: Find g(x), where g(x) is the reflection across the x-axis of f(x)=x. Write your answer in the form ax-h+k, where a, h, and k are integers.

Find g(x), where g(x) is the reflection across the x-axis of f(x)=x.
Write your answer in the form ax-h+k, where a, h, and k are integers.
Transcript text: Find $g(x)$, where $g(x)$ is the reflection across the $x$-axis of $f(x)=|x|$. Write your answer in the form $\mathrm{a}|\mathrm{x}-\mathrm{h}|+\mathrm{k}$, where $\mathrm{a}, \mathrm{h}$, and k are integers.
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Solution

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Solution Steps

To find the reflection of f(x)=x f(x) = |x| across the x x -axis, we need to negate the function f(x) f(x) . This means g(x)=f(x) g(x) = -f(x) . Since f(x)=x f(x) = |x| , the reflection across the x x -axis will be g(x)=x g(x) = -|x| .

Step 1: Define the Original Function

The original function is given by: f(x)=x f(x) = |x|

Step 2: Reflect the Function Across the x x -Axis

To reflect f(x) f(x) across the x x -axis, we negate the function: g(x)=f(x) g(x) = -f(x)

Step 3: Substitute the Original Function

Substitute f(x)=x f(x) = |x| into the equation for g(x) g(x) : g(x)=x g(x) = -|x|

Final Answer

The reflection of f(x)=x f(x) = |x| across the x x -axis is: g(x)=x \boxed{g(x) = -|x|}

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