Understanding Limits of Rational Functions

The video tutorial explains how to determine the limit of a rational function as X approaches a specific value, using direct substitution. It demonstrates the process of checking for discontinuity and verifying the result with a calculator. Additionally, it shows how to use a table of values and a graph to confirm the limit, ensuring the function approaches the same value from both sides.

What is the first step in determining the limit of a rational function as X approaches a specific value?

• Performing a graphical analysis

• Direct substitution

• Checking for asymptotes

• Using L'Hôpital's Rule

What result do we get when we perform direct substitution for the limit as X approaches 6?

• The limit is 128

• The limit is 0

• The limit is undefined

• The limit is infinity

Why is it important to check for discontinuity when finding the limit of a rational function?

• To ensure the function is continuous at the point

• To calculate the integral of the function

• To determine the range of the function

• To find the derivative of the function

How can we verify the limit using a table of values?

• By plotting the function on a graph

• By calculating the integral of the function

• By finding the derivative of the function

• By checking if the values approach a constant as X approaches the limit

What do the function values approach as X approaches 6 from both sides?

• Infinity

• 128

• 6

• 0

What does the graph of the function indicate about the limit as X approaches 6?

• The function has an asymptote at X = 6

• The function value approaches 128

• The function is discontinuous at X = 6

• The function has a hole at X = 6

What is the significance of the Y value at the point where X approaches 6 on the graph?

• It is the maximum value of the function

• It represents a point of discontinuity

• It shows the limit value

• It indicates a vertical asymptote

What is the final conclusion about the limit of the function as X approaches 6?

• The limit is 128

• The limit does not exist

• The limit is infinite

• The limit is 0