Vertical and Horizontal asymptotes of a rational function

The video tutorial explains how to find vertical and horizontal asymptotes in rational functions. It begins with factoring the denominator to identify vertical asymptotes and setting them to zero. The tutorial then covers horizontal asymptotes, focusing on comparing the degrees of the numerator and denominator and using leading coefficients. The video concludes with a brief mention of potential holes in the graph and hints at further problem-solving examples.

What is the process to find vertical asymptotes in a rational function?

• Set the numerator equal to zero.

• Set both numerator and denominator equal to zero.

• Factor the denominator and set it equal to zero.

• Find the derivative of the function.

If a rational function has a numerator and denominator of equal degree, how do you find the horizontal asymptote?

• Use the ratio of the leading coefficients.

• Factor both numerator and denominator.

• Subtract the degrees of numerator and denominator.

• Set the numerator equal to zero.

What is the horizontal asymptote of a function where the leading coefficients of the numerator and denominator are both 1?

• y = x

• y = -1

• y = 0

• y = 1

What is a possible outcome when a factor in the denominator cancels with a factor in the numerator?

• A slant asymptote

• A horizontal asymptote

• A vertical asymptote

• A hole in the graph

Which of the following is NOT a type of asymptote?

• Circular

• Diagonal

• Horizontal

• Vertical