Question

what is the range of the function g(x) = |x – 12| – 2? {y | y > –2} {y | y > –2} {y | y > 12} {y | y > 12}

Answer 1

Range = {y | y ≥ –2}

Answer 2

Answer:

The range of function is $R= \left \{ y|y\geq -2 \right \}$                                                            

Step-by-step explanation:

Given : Function $g(x) = |x -12| -2$

To find : What is the range of the function?

Solution :

The range is defined as the set of y values for which function is defined.

We have given function  $g(x) = |x -12| -2$ in the vertex form.

The general vertex form is $y=a|x-h|+k$ where (h,k) are the vertex of the equation.

On comparing the vertex of the given function is (h,k)=(12,-2)

i.e. The y-values taken is less than -2.

So, the range would be the all y values greater than or equal to -2.

Therefore, The range of function is $R= \left \{ y|y\geq -2 \right \}$

Refer the attached figure below of the function.