Question

The function g(x) is graphed on the coordinate grid.

Which statements are true of g(x)? Check all that apply.

Answer 1

the function g(X) is a translation of
`f(x) = √(x)`

the range is y

the function g(x) can be translated 3 units right and 1 unit up to get the function
`f(x) = √(x)`

Explanation:

Given the graph of a function g(x)

g(x) looks like a square root function

So parent function is
`f(x) = √(x)`

the function g(X) is a translation of
`f(x) = √(x)`

the domain is x

the range is y

The parent function
`f(x) = √(x)` starts at (0,0)

so g(x) is translated 3 units left and 1 unit down

the function g(x) can be translated 3 units right and 1 unit up to get the function
`f(x) = √(x)`

Answer 2

The correct options are 1, 3 and 5.

Explanation:

The given function is a continuous increasing curve which is increasing at decreasing rate. It means it is the graph of a radical function.

Parent radical function is

`f(x)=√(x)`

It means function g(x) is the translation of function
`f(x)=√(x)`. Option 1 is correct.

Domain is the set of input values.

Function is defined for all x ≥ -3.

Domain = x ≥ -3

Option 2 is incorrect.

Range is the set of output values.

The values of the function are always greater than or equal to -1.

Range = y ≥ -1

Option 3 is correct.

The graph of parent function
`f(x)=√(x)` shifts 3 units left and 1 unit down to get the graph of g(x). So the function g(x) is defined as

`f(x)=√(x+3)-1`

Option 4 is incorrect.

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

Option 5 is correct.