Determining the non removable holes of a rational function

The video tutorial explains the concept of domain and discontinuity in rational functions. It highlights how to identify when a function is not defined, leading to discontinuities. The tutorial further explores how to simplify expressions to determine if a discontinuity is a hole, which is removable. It also discusses the domain of functions and the limitations of graphing technology in displaying holes.

What is the first step in identifying a discontinuity in a rational function?

• Calculating the derivative

• Identifying when the function is not defined

• Solving for the y-intercept

• Finding the range of the function

How can you determine if a discontinuity is a hole?

• By finding the limit of the function

• By simplifying the expression and using the division property

• By calculating the second derivative

• By checking if the function is continuous

What happens to the expression when you divide out the discontinuity?

• It becomes undefined

• It results in a hole

• It changes the domain

• It becomes a vertical asymptote

What is a removable discontinuity in the context of rational functions?

• A point where the function is continuous

• A point where the function has a vertical asymptote

• A point where the function is undefined but can be simplified

• A point where the function has a horizontal asymptote

Why might graphing technology not show holes in a function?

• Because holes are too small to be visible

• Because holes are not part of the domain

• Because holes are not considered important

• Because graphing technology only shows continuous functions