Determine the horizontal and vertical asymptotes

The video tutorial explains how to identify removable and non-removable discontinuities in functions, focusing on vertical and horizontal asymptotes. It covers the process of determining the domain and range of a function, emphasizing the absence of discontinuities when the denominator never equals zero. The tutorial also discusses the rules for horizontal asymptotes based on the degree of the numerator and denominator.

What are removable discontinuities in a function?

• Points where the function is undefined

• Points where the function has a vertical asymptote

• Discontinuities that can be factored out

• Discontinuities that cannot be factored out

How do you determine if a vertical asymptote exists?

• By setting the numerator equal to zero

• By setting the denominator equal to zero

• By finding the horizontal asymptote

• By checking if the function is continuous

Why might a vertical asymptote be considered imaginary?

• If the denominator is zero

• If the numerator is zero

• If the solution involves the square root of a negative number

• If the function is continuous

What is the domain of a function with no discontinuities?

• All negative numbers

• All real numbers

• All integers

• All positive numbers

What is the horizontal asymptote when the degree of the numerator is less than the degree of the denominator?

• y = 1

• y = 0

• No horizontal asymptote

• y = x