Learn how to evaluate the limits at infinity with asymptotes on a graph

The video tutorial discusses the concept of infinite discontinuities and asymptotes, focusing on how graphs behave near these asymptotes. It explains that while graphs never cross vertical asymptotes, they can cross horizontal ones. The tutorial also analyzes the behavior of graphs as x approaches positive and negative infinity, highlighting how they taper off towards certain values.

What is an infinite discontinuity in a graph?

• A point where the graph intersects the x-axis

• A point where the graph has an asymptote

• A point where the graph has a hole

• A point where the graph stops

Which type of asymptote can a graph cross?

• Vertical asymptote

• Horizontal asymptote

• Neither vertical nor horizontal asymptotes

• Both vertical and horizontal asymptotes

What does it mean when a graph approaches an asymptote?

• The graph oscillates around the asymptote

• The graph moves away from the asymptote

• The graph gets infinitely close to the asymptote but never touches it

• The graph will eventually intersect the asymptote

As x approaches positive infinity, what behavior does the graph exhibit?

• It rises indefinitely

• It falls indefinitely

• It tapers off to a specific value

• It oscillates without settling

What value does the graph approach as x approaches negative infinity?

• A constant value other than zero

• Zero

• Negative infinity

• Infinity