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 an asymptote?

Back

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

Front

What is a horizontal asymptote?

Back

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

Front

How do you find the horizontal asymptote of a rational function?

Back

1. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0. 2. If the degrees are equal, the horizontal asymptote is 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 happens to the horizontal asymptote when the degree of the numerator is less than the degree of the denominator?

Back

The horizontal asymptote is y=0.

Front

What happens to the horizontal asymptote when the degrees of the numerator and denominator are equal?

Back

The horizontal asymptote is determined by the ratio of the leading coefficients of the numerator and denominator.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the input approaches a certain value, typically where the function is undefined.

Front

How do you find vertical asymptotes in 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 also make the numerator zero.

Front

What is the significance of the leading coefficient in determining horizontal asymptotes?

Back

The leading coefficient helps determine the value of the horizontal asymptote when the degrees of the numerator and denominator are equal.

Front

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

Back

The relationship helps identify the behavior of the function as x approaches infinity or negative infinity.