Identifying Attributes of Rational Functions

Front

What is a rational function?

Back

A function that can be expressed as the ratio of two polynomials.

Front

What is the domain of a rational function?

Back

The set of all real numbers except where the denominator is zero.

Front

What is a vertical asymptote?

Back

A vertical line that the graph approaches but never touches, occurring where the denominator is zero.

Front

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

Back

By comparing the degrees of the numerator and denominator polynomials.

Front

What happens to the graph of a rational function as x approaches infinity?

Back

It approaches the horizontal asymptote.

Front

What is the y-intercept of a function?

Back

The point where the graph crosses the y-axis, found by evaluating the function at x=0.

Front

What is the x-intercept of a function?

Back

The point where the graph crosses the x-axis, found by setting the function equal to zero.

Front

What is the significance of the range of a function?

Back

It represents all possible output values of the function.

Front

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

Back

The function's values increase or decrease without bound as x approaches infinity.

Front

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

Back

If the degree of the numerator is less than the denominator, the horizontal asymptote is y=0.