The graph of f(x) =(square root of "x") 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. a)the functions have the same range. b)the functions have the same domains. c)the only value that is in the domains of both functions is 0. d)there are no values that are in the ranges of both functions. e)the domain of g(x) is all values greater than or equal to 0. f)the range of g(x) is all values less than or equal to 0.

Analysis:

1) The graph of function f(x) = √x is on the first quadrant, because the domain is x ≥ 0 and the range is y ≥ 0

2) The first transformation, i.e. the reflection of f(x) over the x axis, leaves the function on the fourth quadrant, because the new image is y = - √x.

3) The second transformation, i.e. the reflection of y = - √x over the y-axis, leaves the function on the third quadrant, because the final image is - √(-x). This is, g(x) = - √(-x).

From that you have, for g(x):

* Domain: negative x-axis ( -x ≥ 0 => x ≤ 0)

* Range: negative y-axis ( - √(-x) ≤ 0 or y ≤ 0).

Answers:

Now let's examine the statements:

A)The functions have the same range:FALSE the range changed from y ≥ 0 to y ≤ 0

B)The functions have the same domains. FALSE the doman changed from x ≥ 0 to x ≤ 0

C)The only value that is in the domains of both functions is 0. TRUE: the intersection of x ≥ 0 with x ≤ 0 is 0.

D)There are no values that are in the ranges of both functions. FALSE: 0 is in the ranges of both functions.

E)The domain of g(x) is all values greater than or equal to 0. FALSE: it was proved that the domain of g(x) is all values less than or equal to 0.

F)The range of g(x) is all values less than or equal to 0. TRUE: it was proved above.