How to determine if the discontinuities are holes or asymptotes

The video tutorial discusses the concept of discontinuities in precalculus, focusing on holes and asymptotes. It explains how to identify vertical asymptotes by ensuring the denominator is not zero and demonstrates factoring expressions to distinguish between removable and non-removable discontinuities. The tutorial concludes by clarifying that the only vertical asymptote in the example is at x = -2, emphasizing the importance of accurate identification in graph analysis.

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

• Gaps and spikes

• Jumps and breaks

• Holes and asymptotes

• Peaks and troughs

Why is it important to ensure the denominator is not zero when identifying vertical asymptotes?

• To find the x-intercepts

• To determine the y-intercepts

• To simplify the equation

• To avoid undefined expressions

What initial values of x were identified as potential vertical asymptotes?

• x = ±2

• x = ±3

• x = ±4

• x = ±1

What is the true vertical asymptote identified after factoring the expressions?

• x = 4

• x = 2

• x = -2

• x = 0

What is the significance of correctly writing the vertical asymptote in mathematical notation?

• To ensure clarity and accuracy in mathematical communication

• To make the equation look complex

• To confuse the reader

• To add unnecessary details