Respuesta :

Answer:

the function g(X) is a translation of [tex]f(x) = \sqrt{x}[/tex]

the range is {y|y≥-1}

the function g(x) can be translated 3 units right and 1 unit up to get the function [tex]f(x) = \sqrt{x}[/tex]

Step-by-step explanation:

Given the graph of a function g(x)

g(x) looks like a square root function

So parent function is [tex]f(x) = \sqrt{x}[/tex]

the function g(X) is a translation of [tex]f(x) = \sqrt{x}[/tex]

the domain is {x| x ≥ -3}

the range is {y|y≥-1}

The parent function [tex]f(x) = \sqrt{x}[/tex] 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 [tex]f(x) = \sqrt{x}[/tex]

Answer:

The correct options are 1, 3 and 5.

Step-by-step 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

[tex]f(x)=\sqrt{x}[/tex]

It means function g(x) is the translation of function [tex]f(x)=\sqrt{x}[/tex]. Option 1 is correct.

Domain is the set of input values.

Function is defined for all x ≥ -3.

Domain = { x |  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 |  y ≥ -1 }

Option 3 is correct.

The graph of parent function [tex]f(x)=\sqrt{x}[/tex] shifts 3 units left and 1 unit down to get the graph of g(x). So the function g(x) is defined as

[tex]f(x)=\sqrt{x+3}-1[/tex]

Option 4 is incorrect.

The function g(x) can be translated right 3 units and up 1 unit to create the function [tex]f(x)=\sqrt{x}[/tex].

Option 5 is correct.