The 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.'

The true statements:

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.

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Step-by-step explanation:

See the attached figure:

As shown: f(x) = √x with blue color

When f(x) is reflected across the x-axis the result will be (-√x) with red color.

Then the is reflected result across the y-axis to create the graph of function g(x) = -√(-x) with green color.

Domain of f(x) = [0,∞) & Range of f(x) = [0,∞)

Domain of g(x) = (-∞,0] & Range of g(x) = (-∞,0]

So, according to previous, we will check the statements:

1) The functions have the same range. (Wrong)

2) The functions have the same domains. (Wrong)

3) The only value that is in the domains of both functions is 0. (True)

4) There are no values that are in the ranges of both functions. (Wrong)

5) The domain of g(x) is all values greater than or equal to 0. (Wrong)

6) The range of g(x) is all values less than or equal to 0. (True)