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

1 Answer
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
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