# What is the domain and range of (x^3-8)/(x^2-5x+6)?

Feb 2, 2016

The domain is the set of all real values of x except $2$ and $3$

The range is the set of all real values of $y$.

#### Explanation:

The domain of a function is the set of $x$ values for which the function is valid. The range is the corresponding set of $y$ values.

$\frac{{x}^{3} - 8}{{x}^{2} - 5 x + 6}$

=((x-2)(x^2 +2x +4))/((x-3)(x-2)

Thus there is a removable vertical asymptote at $x = 2$ and another vertical asymptote at $x = 3$ because both of these values would make the denominator equal to zero.

The domain is the set of all real values of x except $2$ and $3$

The range is the set of all real values of $y$.