Understanding Limits from Graphs

The video tutorial explains how to find the value of a limit from a graph, covering one-sided limits, limits at specific points, and limits involving vertical and horizontal asymptotes. Through examples, it demonstrates how to determine limits from both the left and right sides and discusses when limits do not exist.

What is a one-sided limit?

• A limit where x approaches from only one side

• A limit that is always zero

• A limit where x approaches from both sides

• A limit that does not exist

If the left and right limits do not match, what can be said about the limit?

• The limit is zero

• The limit is infinite

• The limit exists

• The limit does not exist

How do you determine the value of a function at a specific point on a graph?

• Check the y-axis

• Check the x-axis

• Look for an open circle

• Look for a closed circle

What does it mean if a function is continuous at a point?

• The function has a vertical asymptote

• The left and right limits are different

• The function is undefined at that point

• The left and right limits are the same and equal to the function's value at that point

What happens to the limit as x approaches a vertical asymptote from the left?

• The limit approaches zero

• The limit approaches a finite number

• The limit does not exist

• The limit approaches negative infinity

What is the limit as x approaches a vertical asymptote from the right?

• The limit approaches zero

• The limit approaches a finite number

• The limit approaches positive infinity

• The limit does not exist

What is a horizontal asymptote?

• A vertical line on the graph

• A line that the graph never touches

• A line that the graph approaches as x goes to infinity

• A point where the function is undefined

As x approaches positive infinity, what does the limit approach if there is a horizontal asymptote?

• The limit does not exist

• The limit approaches the y-value of the horizontal asymptote

• The limit approaches zero

• The limit approaches negative infinity

What is the limit as x approaches negative infinity if there is a horizontal asymptote?

• The limit approaches zero

• The limit approaches the y-value of the horizontal asymptote

• The limit approaches positive infinity

• The limit does not exist

What is the significance of a horizontal asymptote in evaluating limits at infinity?

• It has no significance

• It shows where the function is undefined

• It indicates the y-value the function approaches as x becomes very large

• It determines the x-value of the limit