Which statements are true of g(x)? Select three options. The function g(x) is a translation of f(x) = √x. The function g(x) has a domain of x 2-2. The function g(x) has a range …

Question

Which statements are true of g(x)? Select three options.

The function g(x) is a translation of f(x) = √x.
The function g(x) has a domain of x.
The function g(x) has a range of {yly 2-1}.
The function g(x) is represented by the function g(x) =
√x-3-1.
The function g(x) can be translated right 3 units and up
1 unit to create the function f(x) = √x.

Answer 1

The following statements are true of g(x):

1. The function g(x) is a translation of f(x) = Vx. (This statement indicates that g(x) is a transformation of the function f(x) with a vertical translation.)
2. The function g(x) has a domain of {xl× 2-2}. (This statement specifies the domain of g(x) as x ≤ 2 - 2.)
3. The function g(x) can be translated right 3 units and up 1 unit to create the function f(x) = vx. (This statement indicates that by applying a horizontal translation of 3 units to the right and a vertical translation of 1 unit up to g(x), we obtain the function f(x) = Vx.)

The statement "The function g(x) has a range of {yly 2-1}" is not necessarily true based on the information provided. The range of g(x) depends on the specific characteristics and transformations applied to the function f(x). Similarly, the statement "The function g(x) is represented by the function q(x) = Vx-3-1" is not necessarily true as it introduces a new function q(x) that is not mentioned in the original options.