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 general form of a rational function?

Back

The general form of a rational function is f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

Front

What is a vertical asymptote?

Back

A vertical asymptote occurs where the denominator of a rational function is zero, indicating a value that the function cannot take.

Front

How do you find vertical asymptotes?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote indicates the behavior of a function as x approaches infinity or negative infinity.

Front

How do you determine horizontal asymptotes for rational functions?

Back

1. If the degree of the numerator is less than the degree of the denominator, y=0 is the horizontal asymptote. 2. If the degrees are equal, y = leading coefficient of numerator / leading coefficient of denominator. 3. If the degree of the numerator is greater, there is no horizontal asymptote.

Front

What is the significance of the leading coefficient in rational functions?

Back

The leading coefficient affects the end behavior of the graph of the rational function.

Front

What does it mean if a rational function has no horizontal asymptote?

Back

It means that as x approaches infinity or negative infinity, the function's values increase or decrease without bound.

Front

What is the relationship between the degrees of the numerator and denominator in determining asymptotes?

Back

The degrees of the numerator and denominator help determine the existence and location of horizontal and vertical asymptotes.