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.

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.

Solution

Solution Steps

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

Step 1: Define the Original Function

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

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

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

Step 3: Substitute the Original Function

Substitute $ f(x) = |x| $ into the equation for $ g(x) $: \[ g(x) = -|x| \]