How to find the vertical and horizontal asymptotes of a function

The video tutorial explains how to find vertical and horizontal asymptotes in rational functions. It begins with an introduction to asymptotes, followed by a detailed explanation of finding vertical asymptotes by setting the denominator equal to zero. The concept of domain is discussed, highlighting that it includes all real numbers except where the denominator is zero. The tutorial then shifts to horizontal asymptotes, focusing on the degrees of polynomials in the numerator and denominator. It explains that when the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients. The video concludes with a summary of the key steps involved in finding both types of asymptotes.

What is the first step in finding the vertical asymptotes of a rational function?

• Find the derivative of the function

• Integrate the function

• Set the numerator equal to zero

• Set the denominator equal to zero

How is the domain of a function related to its vertical asymptotes?

• The domain includes all real numbers except where the numerator is zero

• The domain is only the negative real numbers

• The domain includes all real numbers except where the denominator is zero

• The domain is only the positive real numbers

How can the domain of a function be expressed if it has a vertical asymptote at x = -1?

• (-∞, -1) ∪ (-1, ∞)

• (-∞, 1) ∪ (1, ∞)

• (-∞, 0) ∪ (0, ∞)

• (-∞, -1) ∪ (0, ∞)

What determines the horizontal asymptote of a rational function when the degrees of the numerator and denominator are equal?

• The ratio of the leading coefficients

• The product of the leading coefficients

• The difference of the leading coefficients

• The sum of the leading coefficients

If the degrees of the numerator and denominator are both 1, what is the horizontal asymptote of the function 2x + 5 / x + 1?

• y = 2

• y = 0

• y = 1

• y = 5