Understanding Asymptotes and Limits

This video tutorial explores the concepts of vertical and horizontal asymptotes using the Desmos graphing calculator. It demonstrates how vertical asymptotes occur when a function approaches infinity at a certain point, and how horizontal asymptotes represent the value a function approaches as x goes to infinity. The video also highlights the differences between these asymptotes, such as the ability of functions to cross horizontal asymptotes but not vertical ones.

What tool is used in the video to explore the relationship between asymptotes and limits?

• Wolfram Alpha

• GeoGebra

• GraphCalc

• Desmos

What happens to the function 2/(x-1) at x=1?

• It becomes undefined

• It equals 1

• It becomes zero

• It equals 2

As x approaches 1 from the left in the function 2/(x-1), what happens to the value of the function?

• It remains constant

• It approaches negative infinity

• It approaches positive infinity

• It approaches zero

What is the horizontal asymptote of the new function as x approaches infinity?

• y = 3

• y = 0

• y = 2

• y = 1

As x approaches negative infinity, what does the function approach?

• It approaches zero

• It approaches three from below

• It remains constant

• It approaches negative three

Which type of asymptote can a function cross?

• Neither

• Both vertical and horizontal

• Horizontal asymptote

• Vertical asymptote

What is a key difference between vertical and horizontal asymptotes?

• Vertical asymptotes are approached as x goes to infinity

• Horizontal asymptotes cannot be crossed

• Vertical asymptotes can be crossed

• Horizontal asymptotes can be crossed

What happens to the function as x approaches positive infinity in terms of horizontal asymptotes?

• It approaches zero

• It diverges

• It oscillates around the asymptote

• It remains constant

In the context of the video, what is the significance of limits in relation to asymptotes?

• Limits help identify the location of asymptotes

• Limits only apply to vertical asymptotes

• Limits determine the slope of the asymptote

• Limits are unrelated to asymptotes

What is the behavior of the function as it oscillates around a horizontal asymptote?

• It gets closer to the asymptote

• It remains constant

• It diverges

• It moves away from the asymptote