Section 7.2: Graph Simple 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 determines the vertical asymptotes of a rational function?

Back

Vertical asymptotes are determined by the values of x that make the denominator equal to zero.

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

To find the horizontal asymptote, compare the degrees of the numerator and denominator polynomials.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What happens to the graph of a rational function at vertical asymptotes?

Back

The graph of a rational function approaches the vertical asymptote but never touches or crosses it.

Front

What is the significance of the horizontal asymptote in a rational function?

Back

The horizontal asymptote indicates the value that the function approaches as x becomes very large or very small.

Front

If the degree of the numerator is less than the degree of the denominator, what is the horizontal asymptote?

Back

The horizontal asymptote is y = 0.

Front

If the degrees of the numerator and denominator are equal, how do you find the horizontal asymptote?

Back

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

Front

What is a slant (oblique) asymptote?

Back

A slant asymptote occurs when the degree of the numerator is exactly one more than the degree of the denominator.