Question

the function graphed is reflected across the x-axis to create a new function.
which is true about the domain and range of each function?
○ both the domain and range change.
○ both the range and domain stay the same.
○ the domain stays the same, but the range changes.
○ the range stays the same, but the domain changes.

Explanation:

1. Domain Analysis: The domain of a function is the set of all valid x-values. Reflecting a graph across the x-axis does not change the set of x-values the function covers, so the domain remains identical for the original and reflected function.
2. Range Analysis: The range of a function is the set of all resulting y-values. Reflecting across the x-axis negates every y-value of the original function. For the given graph, the original range is $y \geq 2$. After reflection, the new range becomes $y \leq -2$, so the range changes.

Answer:

The domain stays the same, but the range changes.