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 does it mean to simplify a rational function?

Back

Simplifying a rational function involves factoring the numerator and denominator and canceling out any common factors.

Front

How do you find common factors in a rational function?

Back

To find common factors, factor both the numerator and denominator completely and identify any factors that appear in both.

Front

What is the importance of identifying restrictions in rational functions?

Back

Identifying restrictions is crucial because it determines the values for which the function is undefined, typically where the denominator equals zero.

Front

What is the process of factoring a polynomial?

Back

Factoring a polynomial involves rewriting it as a product of its factors, which can include numbers, variables, or other polynomials.

Front

How do you cancel out common factors in rational functions?

Back

To cancel out common factors, divide both the numerator and denominator by the common factor, simplifying the expression.

Front

What is the vertical asymptote of a rational function?

Back

A vertical asymptote occurs at values of x that make the denominator zero, indicating where the function approaches infinity.

Front

What is the horizontal asymptote of a rational function?

Back

The horizontal asymptote describes the behavior of a rational function as x approaches infinity, determined by the degrees of the numerator and denominator.

Front

What is the difference between a removable and non-removable discontinuity?

Back

A removable discontinuity occurs when a factor cancels out, while a non-removable discontinuity occurs at values that make the denominator zero without cancellation.

Front

How do you determine the end behavior of a rational function?

Back

The end behavior can be determined by analyzing the degrees of the numerator and denominator and their leading coefficients.