Question

What happens to the x-intercepts of the function y = x? - 25 when the
graph is reflected over the x-axis? Explain.

• The x-intercepts become negated.
• Treetin eves reain the same because the y-values get negated during
• The x-values and y-values switch.
• This function does not have any x-intercepts, so no changes are necessary.

Answer 1

To determine what happens to the x-intercepts of the function \( y = x - 25 \) when the graph is reflected over the x-axis, we first need to identify the x-intercepts of the original function.

1. **Finding the x-intercepts of \( y = x - 25 \)**:
The x-intercept occurs when \( y = 0 \). Setting \( y = 0 \):
\[
0 = x - 25 \\
x = 25
\]
So, the x-intercept of the function \( y = x - 25 \) is at the point (25, 0).

2. **Reflecting over the x-axis**:
When a graph is reflected over the x-axis, the y-values of all points on the graph are negated. Therefore, the new function after reflection would be:
\[
y = -(x - 25) = -x + 25
\]

3. **Finding the new x-intercepts**:
To find the x-intercepts of the reflected function \( y = -x + 25 \):
\[
0 = -x + 25 \\
x = 25
\]
The x-intercept remains at (25, 0).

### Conclusion:
The x-intercepts remain the same because the x-values do not change when reflecting over the x-axis—only the y-values are negated. Therefore, the correct explanation is:

- **The x-intercepts remain the same because the y-values get negated during reflection.**