Question

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

Answer 1

Answer:

$\left \{ y|y\geq -2 \right \}$

Step-by-step explanation:

The function is given by $g(x)=|x-12|-2$

It is an absolute value function which has a v- shaped graph.

The vertex form of an absolute function is given by y = a|x-h| +k, where (h,k) is the vertex.

Comparing the given equation with this, we have

h = 12

k = -2

Hence, the vertex would be (12,-2).

Now, the range of the function is the set of y values for which the function is defined.

This function has vertex of (12,-2). hence, it would not be take any values which are less than -2. Please see the attache graph.

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

Hence, range is given by $\left \{ y|y\geq -2 \right \}$

Answer 2

The range of the function $g(x)=|x-12|-2$ is $\boxed{[-2,\infty)}$

Further explanation:

Given:

The function is given as follows:

$\boxed{g(x)=|x-12|-2}$

The function $g(x)$ is an absolute value function.

If $x\leq12$ then the function $g(x)$ can be written as follows:

$\boxed{g(x)=-(x-12)-2}$

Now, simplify the function $g(x)=-(x-12)-2$ as follows:

$\begin{aligned}g(x)&=-(x-12)-2\\&=-x+12-2\\&=-x+10\end{aligned}$

For $x\leq12$, the equation is

$g(x)=-x+10$                  …… (1)

Put $x=12$ in the equation (1) to obtain the value of $g(12)$.

$\begin{aligned}g(12)&=-12+10\\&=-2\end{aligned}$

Therefore, the minimum value of the function $g(x)=-x+10$ is $-2$.

If $x\geq12$ then the function $g(x)$ can be written as follows:

$\boxed{g(x)=(x-12)-2}$

Now, simplify the function $g(x)=(x-12)-2$ as follows:

$\begin{aligned}g(x)&=(x-12)-2\\&=x-12-2\\&=x-14\end{aligned}$  

For $x\geq12$ the equation is,

$g(x)=x-14$                    …… (2)

Put $x=12$ in equation (2) to obtain the value of $g(12)$.

$\begin{aligned}g(12)&=12-14\\&=-2\end{aligned}$

Therefore, the minimum value of the function $g(x)$ is $-2$.

The minimum value of the function $g(x)=|x-12|-2$ is $-2$ and the maximum value is infinite.

The range of the function is the set of value of function at which the function is defined.

Thus the range of the function $g(x)=|x-12|-2$ is $\boxed{[-2,\infty)}$.

Learn more:

1. A problem on range of a function brainly.com/question/3412497

2. A problem on function brainly.com/question/2142762

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Function

Keywords:  g(x)=|x-12|-2, range, g(x)=-(x-12)-2, g(x)=(x-12)-2, function, domain, absolute value of function, minimum value, maximum value, modulus, modulus function, range, domain.