How do you find the domain and range of #f(x)= sqrt(x+6)/(x-5)#?

1 Answer
Jul 27, 2015

Answer:

Domain : the fraction and the root give limitations:

Explanation:

#x>=-6# or the argument under the square root will be negative.
#x!=5# or the denominator will be #=0#

Range : when #x=-6->f(x)=0#, but on the right side of the two-armed graph #x=0# is a horizontal asymtote.
#lim_(x-> oo) f(x)=0#
As #x# nears #5#, #f(x)# gets very large:
#lim_(x->5-) f(x)=-oo# and #lim_(x->5+) f(x)=+oo#

So there are no restrictions on the range.
graph{sqrt(x+6)/(x-5) [-5.04, 27.01, -8.67, 7.37]}