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∣
Final Answer
The reflection of f(x)=∣x∣ across the x-axis is:
g(x)=−∣x∣