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

1 Answer
Alan P.
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#

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