Chapter 1, Problem 27RE

(a)

To determine

To find: The domain of the function $y=\left|x\right|-2$ .

Answer to Problem 27RE

The domain of the function $y=\left|x\right|-2$ is set of real numbers or the interval $\left(-\infty ,\infty \right)$ .

Explanation of Solution

Given information:

The given function is $y=\left|x\right|-2$ .

Calculation:

Domain is the set of all input values such that the function is define.

The function $y=\left|x\right|-2$ is defined for all the real values of $x$ .

Therefore, the domain of the function $y=\left|x\right|-2$ is set of real numbers or the interval $\left(-\infty ,\infty \right)$ .

(b)

To determine

To find: The range of the function $y=\left|x\right|-2$ .

Answer to Problem 27RE

The range of the function $y=\left|x\right|-2$ is the interval $\left[-2,\infty \right)$ .

Explanation of Solution

Given information:

The given function is $y=\left|x\right|-2$ .

Calculation:

The value of the function $f\left(x\right)=\left|x\right|$ is always greater than or equal to $0$ .

Subtract $2$ from both the sides.

  $y=\left|x\right|-2$

The value of the function $y=\left|x\right|-2$ is greater than or equal to $-2$ .

Therefore, the range of the function $y=\left|x\right|-2$ is the interval $\left[-2,\infty \right)$ .

(c)

To determine

To graph: The function $y=\left|x\right|-2$ .

Explanation of Solution

Given information:

The given functionis $y=\left|x\right|-2$ .

Graph:

To graph a function $y=\left|x\right|-2$ , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press $\boxed{\text{Y}=}$ key and enter right hand side of the equation $y=\left|x\right|-2$ after the symbol ${\text{Y}}_1$ . Enter the keystrokes $\boxed{\text{MATH}}\boxed{\to }\boxed{1}\boxed{\text{X}}\boxed{)}\boxed{-}\boxed{2}$ .

The display will show the equation,

  ${\text{Y}}_{\text{1}}=\text{abs}\left(\text{X}\right)-2$

Now, press the $\boxed{\text{GRAPH}}$ key and $\boxed{\text{TRACE}}$ key to produce the graph of both the equations as shown below.

  

Figure (1)

Interpretation: From the above graph it can be observed that the graph is symmetric about the y -axis.