Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What is the horizontal asymptote of a rational function?

Back

The horizontal asymptote is a horizontal line that the graph of the function approaches as x approaches positive or negative infinity.

Front

How do you find the vertical asymptotes of a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator equal to zero, provided that these values do not cancel with the numerator.

Front

What is an asymptote?

Back

An asymptote is an imaginary line that a graph approaches but never touches.

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except for the values that make the denominator zero.

Front

What is the range of a rational function?

Back

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

Front

How do you solve rational equations?

Back

To solve rational equations, find a common denominator, multiply through by that denominator to eliminate fractions, and then solve the resulting equation.

Front

What is the least common denominator (LCD)?

Back

The least common denominator is the smallest expression that can be used as a common denominator for a set of fractions.

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where the denominator is zero, as division by zero is not possible.

Front

What is a hole in a rational function?

Back

A hole occurs in the graph of a rational function at a point where both the numerator and denominator are zero, indicating a removable discontinuity.