Question

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

Answer 1

(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
`color(white)("XXX")`Domain: `x in (-oo,-4) uu (-4,+oo)`

`color(white)("XXX")`Range: `f(x) in {-1,+1}`

When `x=0`
`color(white)("XXX")f(x)=+1`
So the `y` (or `f(x)`) intercept is `+1`

`f(x) !=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`