Understanding Rational Functions and Asymptotes

This video tutorial covers rational functions, focusing on their components, domain, zeros, and discontinuities. It explains vertical and horizontal asymptotes, removable discontinuities, and provides examples to illustrate these concepts. The video also discusses how to determine horizontal asymptotes by comparing the degrees of the numerator and denominator, and introduces slant asymptotes for improper rational functions.

What is a rational function?

• A function that can be expressed as a sum of integers.

• A function that has a numerator and a denominator, both of which are polynomials.

• A function that can be expressed as a product of integers.

• A function that is always positive.

Which values must be excluded from the domain of a rational function?

• Values that make the function undefined.

• Values that make the denominator zero.

• Values that make the numerator zero.

• Values that make both the numerator and denominator zero.

How do you find the zeros of a rational function?

• By finding values that make the denominator zero.

• By finding values that make the function undefined.

• By finding values that make the numerator zero.

• By finding values that make both the numerator and denominator zero.

What is a vertical asymptote?

• A point where the graph intersects the x-axis.

• A point where the graph intersects the y-axis.

• A vertical line that the graph approaches but never crosses.

• A horizontal line that the graph approaches but never touches.

How do you determine if a rational function has a horizontal asymptote?

• By checking if the function is continuous.

• By comparing the degrees of the numerator and denominator.

• By finding the zeros of the numerator.

• By finding the zeros of the denominator.

What is a slant asymptote?

• A point where the graph intersects the x-axis.

• A slanted line that the graph approaches but never crosses.

• A vertical line that the graph approaches but never crosses.

• A horizontal line that the graph approaches but never touches.

What is the first step in analyzing a rational function?

• Finding the zeros of the function.

• Finding the domain of the function.

• Determining the asymptotes.

• Factoring the numerator and denominator.