Question

he graph of f(x) = StartRoot x EndRoot is reflected across the x-axis and then across the y-axis to create the graph of function g(x). Which statements about the functions f(x) and g(x) are true? Check all that apply.

The functions have the same range.
The functions have the same domains.
The only value that is in the domains of both functions is 0.
There are no values that are in the ranges of both functions.
The domain of g(x) is all values greater than or equal to 0.
The range of g(x) is all values less than or equal to 0.

Answer 1

g(x) is obtained by y = sqrt(x) → reflect across x-axis: y = −sqrt(x) → reflect across y-axis: y = −sqrt(−x). So

- f: domain x ≥ 0, range y ≥ 0.
- g: domain x ≤ 0, range y ≤ 0.

Thus the true statements are:
- The only value that is in the domains of both functions is 0.
- The range of g(x) is all values less than or equal to 0.

All other statements are false.