A2 Rational Functions & Equations

Front

Define 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 domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator equals zero.

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes occur at values of x that make the denominator zero, provided that the numerator is not also zero at those points.

Front

Back

Front

Back

x cannot equal to -2.

Front

Fully factor the expression: 25x^2 - 81

Back

(5x+9)(5x-9)

Front

Back

Front

What is a horizontal asymptote?

Back

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

Front

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

Back

Compare the degrees of the numerator and denominator: If the degree of the numerator is less, y=0; if equal, y= leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Front

What is the significance of the x-intercept in a rational function?

Back

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