# How do you graph, find the zeros, intercepts, domain and range of f(x)=abs(x+4)/(x+4)?

Oct 9, 2017

(see below)

#### Explanation:

By inspection
color(white)("XXX")abs(x+4)/(x+4){(=-1,color(white)("xxx"),"if " x < -4),("is undefined",,"if "x=0),(=+1,,"if " x > -4):}

Therefore
$\textcolor{w h i t e}{\text{XXX}}$Domain: $x \in \left(- \infty , - 4\right) \cup \left(- 4 , + \infty\right)$

$\textcolor{w h i t e}{\text{XXX}}$Range: $f \left(x\right) \in \left\{- 1 , + 1\right\}$

When $x = 0$
$\textcolor{w h i t e}{\text{XXX}} f \left(x\right) = + 1$
So the $y$ (or $f \left(x\right)$) intercept is $+ 1$

$f \left(x\right) \ne 0$ for any value of $x$
Therefore there is no $x$ intercept.
(this is also the response to the request for zeros; since $x$ intercepts and zeros are the same thing).

Your graph should look something like:
graph{abs(x+4)/(x+4) [-9.23, 1.87, -3.02, 2.53]}
...although I would try to be absolutely clear that there is no solution at $x = - 4$