Understanding Asymptotes in Rational Functions

This video tutorial covers the identification and graphing of asymptotes in rational functions. It explains how to find vertical, horizontal, and slant asymptotes, and how to graph these functions. The tutorial also discusses determining the domain and range of rational functions and provides examples to illustrate these concepts.

What is the vertical asymptote of the function y = 1/(x-3)?

• x = -3

• x = 3

• x = 0

• x = 1

For the function y = 1/(x-3), what is the horizontal asymptote?

• y = 1

• y = -3

• y = 3

• y = 0

In the function y = 1/(x+2) + 7, what is the vertical asymptote?

• x = -2

• x = 0

• x = 2

• x = 7

What is the horizontal asymptote of the function y = 1/(x+2) + 7?

• y = 7

• y = -7

• y = 0

• y = 2

For the function y = (6x-18)/(2x+4), what is the horizontal asymptote?

• y = 3

• y = 0

• y = -3

• y = 6

What is the vertical asymptote of the function y = (6x-18)/(2x+4)?

• x = 2

• x = 3

• x = -2

• x = 0

In the function y = (2x^2 - 3x - 2)/(x^2 + x - 6), what is the vertical asymptote?

• x = 2

• x = -3

• x = 3

• x = -2

What is the horizontal asymptote of the function y = (2x^2 - 3x - 2)/(x^2 + x - 6)?

• y = 1

• y = -2

• y = 0

• y = 2

For the function y = (2x^2 - x + 1)/(x - 2), what type of asymptote is present?

• Slant

• Horizontal

• Vertical

• None

What is the vertical asymptote of the function y = (2x^2 - x + 1)/(x - 2)?

• x = 2

• x = -2

• x = 1

• x = 0