How do you find the domain and range of f(x)= sqrt(x+6)/(x-5)f(x)=x+6x5?

1 Answer
Jul 27, 2015

Domain : the fraction and the root give limitations:

Explanation:

x>=-6x6 or the argument under the square root will be negative.
x!=5x5 or the denominator will be =0=0

Range : when x=-6->f(x)=0x=6f(x)=0, but on the right side of the two-armed graph x=0x=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]}