Rational Functions Domain and Range

Front

What is the domain of a rational function?

Back

The domain of a rational function is the set of all real numbers except where the denominator is zero.

Front

What is the range of a rational function?

Back

The range of a rational function is the set of all real numbers except for any values that the function cannot take, often determined by horizontal asymptotes or excluded values.

Front

How do you find the domain of the function f(x) = \frac{2x - 1}{3x + 6}?

Back

Set the denominator equal to zero: 3x + 6 = 0. Solve for x to find that x cannot equal -2.

Front

What is the domain of the function y = \frac{1}{x}?

Back

The domain is all real numbers except x = 0.

Front

What is the range of the function y = \frac{1}{x}?

Back

The range is all real numbers except y = 0.

Front

Identify the domain of the function f(x) = -\frac{1}{x + 3}.

Back

Domain: (-\infty, -3) U (-3, \infty) because x cannot equal -3.

Front

Identify the range of the function f(x) = -\frac{1}{x + 3}.

Back

Range: (-\infty, 0) U (0, \infty) because the function never reaches 0.

Front

What is the domain of the function y = \frac{x^2 + 5x + 6}{x + 2}?

Back

The domain is all real numbers except x = -2.

Front

What is the range of the function y = \frac{x^2 + 5x + 6}{x + 2}?

Back

The range is all real numbers except y = -2.

Front

What is a vertical asymptote in the context of rational functions?

Back

A vertical asymptote occurs at values of x that make the denominator zero, indicating where the function approaches infinity.