Asymptotes of Rational Functions

The video tutorial covers the process of graphing rational functions by identifying vertical and horizontal asymptotes. It explains how to find these asymptotes by setting the denominator to zero and comparing the degrees of the numerator and denominator. The tutorial includes several examples, ranging from simple to complex functions, demonstrating how to plot points and draw graphs accurately.

What is the first step in graphing a rational function?

• Plot random points

• Determine the y-intercepts

• Locate the vertical asymptotes

• Find the x-intercepts

How do you find a vertical asymptote of a rational function?

• Find the x-intercepts

• Set the denominator equal to zero

• Find the y-intercepts

• Set the numerator equal to zero

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

• The sum of the coefficients

• The difference of the coefficients

• The ratio of the leading coefficients

• The product of the coefficients

In Example 1, what is the vertical asymptote of the function x - 1 / x + 2?

• x = -2

• x = 1

• x = 2

• x = -1

In Example 1, what is the horizontal asymptote of the function x - 1 / x + 2?

• y = 0

• y = -1

• y = 1

• y = 2

In Example 2, what is the vertical asymptote of the function -4 / x - 3?

• x = 4

• x = -4

• x = 3

• x = -3

In Example 2, what is the horizontal asymptote of the function -4 / x - 3?

• y = 0

• y = 1

• y = -1

• y = 4

In Example 3, how many vertical asymptotes does the function have?

• Two

• Three

• One

• None

In Example 3, what is the horizontal asymptote of the function?

• y = 0

• y = -1

• y = 2

• y = 1

In Example 4, what is the vertical asymptote of the function?

• x = 2.5

• x = 1.5

• x = -2.5

• x = -1.5