# How do you find domain and range for #f(x)=x/(x^3+8) #?

##### 1 Answer

Sep 22, 2015

Domain =

Range =

#### Explanation:

First factorize the denominator to find possible points of discontinuity.

Factorize it as a sum of 2 cubes, and then as a trinomial to get

The trinomial in the denominator is an irreducible quadratic and has no real roots.

Hence the only vertical asymptote is at

The horizontal asymptote would usually occur at

However in this case, 0 is in the range of the function since x = 0 in the numerator would set the output value y to 0.

So the domain is all real numbers x except -2, and the range is all real numbers y

Graphically :

graph{x/(x^3+8) [-10, 10, -5, 5]}