QuestionGraph $f(x)=\frac{|x+2|}{x+2}$ for the range $[-4,4]$ .

Studdy Solution

STEP 1

Assumptions1. $f(x)$ is a function defined as $f(x)=\frac{|x+|}{x+}$ . . We are asked to sketch the graph of $f(x)$ on the interval $[-4,4]$ .

STEP 2

The function $f(x)$ is not defined for $x=-2$ because the denominator becomes zero at $x=-2$ . So, we will consider two cases separately $x<-2$ and $x>-2$ .

STEP 3

When $x<-2$ , $x+2<0$ . Therefore, $|x+2|=-(x+2)$ . So, $f(x)$ becomes $f(x)=\frac{|x+2|}{x+2}=\frac{-(x+2)}{x+2}=-1$

STEP 4

When $x>-2$ , $x+2>0$ . Therefore, $|x+2|=x+2$ . So, $f(x)$ becomes $f(x)=\frac{|x+2|}{x+2}=\frac{x+2}{x+2}=1$

STEP 5

Now, we can sketch the graph of $f(x)$ on the interval $[-4,4]$ . For $x<-2$ , $f(x)=-1$ and for $x>-2$ , $f(x)=1$ . At $x=-2$ , $f(x)$ is not defined.

STEP 6

The graph of $f(x)$ will be a horizontal line at $y=-1$ for $x<-2$ and a horizontal line at $y=1$ for $x>-2$ . At $x=-2$ , there will be a hole indicating that $f(x)$ is not defined.

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