Find g(x), where g(x) is the reflection across the x-axis of f(x)=
–
x+4.
Write your answer in the form mx+b, where m and b are integers.

The function \( g(x) \) is the reflection of \( f(x) = -x + 4 \) across the x-axis. To reflect a function across the x-axis, you multiply the entire function by \(-1\).

Given:
\[
f(x) = -x + 4
\]

The reflection across the x-axis is:
\[
g(x) = -f(x) = -(-x + 4)
\]

Simplify:
\[
g(x) = x - 4
\]

Thus, the reflected function is:
\[
g(x) = x - 4
\]

### Do you want details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you reflect a function across the y-axis?
2. What is the effect of reflecting the function \( f(x) = x^2 \) across the x-axis?
3. How do you reflect a function across the line \( y = x \)?
4. What happens if you reflect a function across both the x-axis and y-axis?
5. Can a function ever be identical to its reflection across the x-axis?

**Tip:** Reflecting a function across the x-axis simply changes the sign of the output of the function, but keeps the inputs the same.

Find g(x), where g(x) is the reflection across the x-axis of f(x) = -x + 4. Write your answer in the form mx+b, where m and b are integers.

Learn how to reflect the linear function f(x) = -x + 4 across the x-axis. This detailed solution covers key mathematical concepts including reflections and linear equations, suitable for students in Grades 9-10.

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