How to determine if discontinuities are holes or asymptotes

The video tutorial discusses the concepts of discontinuities in precalculus, focusing on holes and asymptotes. It explains how to identify vertical asymptotes by setting the denominator to zero and factoring expressions to find removable discontinuities. The tutorial concludes by determining the real vertical asymptotes and provides a cautionary note on correctly identifying them.

What are the two types of discontinuities discussed in the video?

• Holes and jumps

• Holes and asymptotes

• Removable and non-removable

• Asymptotes and jumps

What condition must be met for a vertical asymptote to occur?

• The numerator equals zero

• The function is undefined

• The denominator equals zero

• The function is continuous

How do you determine if a discontinuity is removable?

• By checking if the numerator can be factored

• By checking if the denominator can be factored

• By solving the equation for the numerator

• By solving the equation for the denominator

What is the true vertical asymptote identified in the example?

• X = -4

• X = 2

• X = -2

• X = 4

What is the significance of X + 2 in the context of the graph?

• It represents a pole

• It represents a jump

• It represents a hole

• It represents a removable discontinuity