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

1 Answer
Roella W.
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.

(x^3 - 8)/(x^2 - 5x +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.

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