Find the domain and range of

Question

(2x + 24)/(3x - 3)?

Answer 1

The rational function f(x) = (2x + 24)/(3x - 3)

We know that all possible values of x  is domain of a function.

A rational function is simply fraction and in a fraction the denominator cannot be equal to 0 because it would be undefined.

To find which number make the fraction undefined create an equation where the denominator is not equal to zero.

3x - 3 ≠ 0

3x ≠ 3

x ≠ 1

So the domain of the function all real numbers except x ≠ 1.

Domain set is {x ∈ R : x ≠ 1}.

To determine the range, find the horizontal asymptote of function.

To find horizontal asymptote, first find the degree of the numerator and  the degree of denominator.

Degree of the numerator = 1 and the degree of denominator = 1.

Since the degree of the numerator is equal to the degree of the denominator, horizontal asymptote is the ratio of the leading coefficient of numerator and denominator.

Leading coefficient of numerator = 2, leading coefficient of denominator = 3

y = 2/3

y = 2/3 is the horizontal asymptote.

So the range of the function is {y ∈ R : y ≠ 2/3}.