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 is f(x) = P(x) / Q(x), where P(x) and Q(x) are polynomials.

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines x = a where the function approaches infinity or negative infinity as x approaches a.

Front

How do you find vertical asymptotes of a rational function?

Back

Set the denominator Q(x) = 0 and solve for x.

Front

What are x-intercepts of a rational function?

Back

X-intercepts are points where the graph of the function crosses the x-axis, found by setting the numerator P(x) = 0.

Front

How do you find x-intercepts of a rational function?

Back

Set the numerator P(x) = 0 and solve for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that the graph approaches as x approaches infinity or negative infinity.

Front

How do you determine horizontal asymptotes for rational functions?

Back

Compare the degrees of the numerator and denominator: If degree of P < degree of Q, y = 0; if degree of P = degree of Q, y = leading coefficient of P / leading coefficient of Q.

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial, similar to numerical long division.

Front

When do you use polynomial long division with rational functions?

Back

Use polynomial long division when the degree of the numerator is greater than or equal to the degree of the denominator.