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.
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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).
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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: \[ y = -(x - 25) = -x + 25 \]
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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.