End Behavior and Rational Function Concepts

Front

What is the end behavior of a rational function?

Back

The end behavior of a rational function describes how the function behaves as the input values approach positive or negative infinity. It is determined by the degrees of the numerator and denominator.

Front

Define asymptote in the context of rational functions.

Back

An asymptote is a line that a graph approaches but never touches. In rational functions, vertical asymptotes occur where the denominator is zero, and horizontal asymptotes describe the behavior of the function as x approaches infinity.

Front

Factor the expression: 3a^2 + 4a + 1

Back

(3a + 1)(a + 1)

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = k where the function approaches infinity or negative infinity as x approaches k.

Front

What is a horizontal asymptote?

Back

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

Front

Factor the expression: 5n^2 - 6n - 27

Back

(5n + 9)(n - 3)

Front

What does it mean for a function to be not factorable?

Back

A function is not factorable if it cannot be expressed as a product of simpler polynomials with real coefficients.

Front

Factor the expression: x^2 + 7x + 12

Back

(x + 3)(x + 4)

Front

What is the significance of the degree of a polynomial in rational functions?

Back

The degree of a polynomial in the numerator and denominator determines the end behavior and the number of asymptotes of the rational function.

Front

What is the end behavior of the function as x approaches infinity for the function f(x) = (2x^2 + 3)/(x^2 + 1)?

Back

As x approaches infinity, f(x) approaches 2.