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

1 Answer
MeneerNask ยท Jim H
Jul 27, 2015

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]}

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