What is the range of the function #f(x) = 5/(x-3)#?

1 Answer
Jan 8, 2017

Answer:

The range of #f(x)# is #R_f(x)=RR-{0}#

Explanation:

The domain of #f(x)# is #D_f(x)=RR-{3}#

To determine the range, we calculate the limit of #f(x)# as #x->+-oo#

#lim_(x->-oo)f(x)=lim_(x->-oo)5/x=0^-#

#lim_(x->+oo)f(x)=lim_(x->+oo)5/x=0^+#

Therefore the range of #f(x)# is #R_f(x)=RR-{0}#

graph{5/(x-3) [-18.02, 18.01, -9, 9.02]}