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The problem asks for the equation that shows the reflection of the function \( f(x) = 3x - 5 \) over the x-axis.

When a function is reflected over the x-axis, the y-values (or the output of the function) are multiplied by \(-1\). Mathematically, this means we change the sign of the entire function.

The given function is:

\[
f(x) = 3x - 5
\]

To reflect this over the x-axis, we multiply the entire function by \(-1\):

\[
- \left( 3x - 5 \right) = -3x + 5
\]

The correct equation that shows this reflection is:

\[
-3x + 5
\]

Looking at the choices provided:

- The correct answer is the last option: **\(-3x - 5\)**.

Would you like a deeper explanation or have any questions?

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Here are 5 related questions to expand on this:

1. What happens when a function is reflected over the y-axis?
2. How do vertical and horizontal shifts affect a function's graph?
3. Can you reflect more complex functions like quadratics or trigonometric functions?
4. How does scaling affect a graph compared to reflection?
5. How do you reflect a function over a line other than the x-axis?

**Tip**: When reflecting over the x-axis, remember that all the output values (y-values) change their sign.

Given the following equation f(x) = 3x - 5, select the correct equation that shows that the equation reflects over the x-axis.

Explore how to reflect the linear function f(x) = 3x - 5 over the x-axis by multiplying the function by -1. Understand the process of function reflection and find the correct reflected equation. Suitable for students in Grades 9-12.

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