Graphing 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 in the context of rational functions?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

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

Back

The horizontal asymptote can be determined by comparing the degrees of the numerator and denominator polynomials.

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 degree of the numerator is equal to the degree of the denominator?

Back

The horizontal asymptote is y = the ratio of the leading coefficients of the numerator and denominator.

Front

What happens to the horizontal asymptote when the degree of the numerator is greater than the degree of the denominator?

Back

There is no horizontal asymptote; the function may have an oblique asymptote instead.

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.

Front

How do you find the coordinates of a hole in a rational function?

Back

To find the coordinates of a hole, factor the numerator and denominator, cancel the common factors, and evaluate the function at the x-value of the canceled factor.

Front

What are x-intercepts in a rational function?

Back

X-intercepts are the points where the graph of the function crosses the x-axis, found by setting the numerator equal to zero.