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?

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.