The function g(x) is graphed on the coordinate grid. Which statements are true of g(x)? Select three options.

A. The function g(x) is a translation of f(x) = /sqrt x.

B. The function g(x) has a domain of {x | x > –2}.

C. The function g(x) has a range of {y | y > –1}.

D. The function g(x) is represented by the function g(x) = /sqrt x - 3 - 1.

E. The function g(x) can be translated right 3 units and up 1 unit to create the function f(x) = /sqrt x.

A. The function g(x) is a translation of f(x) = √x.
C. The function g(x) has a range of {y | y > –1}.
E. The function g(x) can be translated right 3 units and up 1 unit to create the function f(x) = √x

Explanation:

The function f(x) = √x has been translated 3 units to the left and 1 unit down to make g(x). That means translating g(x) 3 units right and 1 unit up will make f(x). (matches choices A and E)

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The range of the function is the vertical extent, all y-values ≥ -1. (matches choice C)

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The translated function is ...

g(x) = f(x+3) -1 = √(x +3) -1 . . . . . does not match choice D

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The domain of the function is the horizontal extent, all x-values ≥ -3. (does not match choice B)