How do you find the domain and range of #f(x) = (x-4)/(x+3) #?

1 Answer
Mar 7, 2017

Answer:

The domain is #x!=-3# as this would make the denominator #=0#.
There are no other restrictions.

Explanation:

For the range we look at what happens when #x->+-oo#
In both cases the fraction will approach #f(x)=+1#, but will never get there. #y!=+1#

In short:
#lim_(x->-3^-)f(x)=+oo# and #lim_(x->-3^+)f(x)=-oo#

#lim_(x-> -oo)f(x)=lim_(x->+oo)f(x)=+1#

#x=-3# and #y=+1# are called the asymptotes .
graph{(x-4)/(x+3) [-25.65, 25.65, -12.82, 12.84]}