Question
What happens to the x-intercepts of the function y=x2−25
when the graph is reflected over the x-axis? Explain.(1 point)
Responses
The x-intercepts become negated.
The x -intercepts become negated.
The x-intercepts remain the same because the y-values get negated during a reflection over the x-axis.
The x -intercepts remain the same because the y -values get negated during a reflection over the x -axis.
This function does not have any x-intercepts, so no changes are necessary.
This function does not have any x -intercepts, so no changes are necessary.
The x-values and y-values switch.
when the graph is reflected over the x-axis? Explain.(1 point)
Responses
The x-intercepts become negated.
The x -intercepts become negated.
The x-intercepts remain the same because the y-values get negated during a reflection over the x-axis.
The x -intercepts remain the same because the y -values get negated during a reflection over the x -axis.
This function does not have any x-intercepts, so no changes are necessary.
This function does not have any x -intercepts, so no changes are necessary.
The x-values and y-values switch.
Answers
GPT-4o mini
To analyze what happens to the x-intercepts of the function \( y = x^2 - 25 \) when the graph is reflected over the x-axis, we first need to determine the x-intercepts of the function.
The x-intercepts occur where \( y = 0 \):
\[
0 = x^2 - 25
\]
Solving for \( x \):
\[
x^2 = 25
\]
\[
x = 5 \quad \text{or} \quad x = -5
\]
So the x-intercepts are at \( (5, 0) \) and \( (-5, 0) \).
When the graph is reflected over the x-axis, the y-values are negated. However, since the y-values for the x-intercepts are both \( 0 \) (the points are on the x-axis), negating \( 0 \) still gives \( 0 \). Therefore, the x-intercepts themselves do not change in their positions.
Thus, the correct response is:
**The x-intercepts remain the same because the y-values get negated during a reflection over the x-axis.**
The x-intercepts occur where \( y = 0 \):
\[
0 = x^2 - 25
\]
Solving for \( x \):
\[
x^2 = 25
\]
\[
x = 5 \quad \text{or} \quad x = -5
\]
So the x-intercepts are at \( (5, 0) \) and \( (-5, 0) \).
When the graph is reflected over the x-axis, the y-values are negated. However, since the y-values for the x-intercepts are both \( 0 \) (the points are on the x-axis), negating \( 0 \) still gives \( 0 \). Therefore, the x-intercepts themselves do not change in their positions.
Thus, the correct response is:
**The x-intercepts remain the same because the y-values get negated during a reflection over the x-axis.**