Graphing Rational Functions With Vertical, Horizontal & Slant Asymptotes, Holes, Domain & Range

Created from Youtube video: https://www.youtube.com/watch?v=XE-Z2-F3oWwvideo

Concepts covered:rational functions, asymptotes, domain and range, graphing, holes

The video provides a comprehensive guide on graphing rational functions, focusing on identifying and plotting vertical, horizontal, and slant asymptotes, as well as determining holes, domain, and range. It explains the process of finding asymptotes and holes, and how to accurately sketch graphs of rational functions, including examples with different types of asymptotes and transformations.

chapter

Concepts covered:rational functions, asymptotes, domain and range, graphing, holes

Question 1

A vertical asymptote occurs where the denominator equals zero.

Question 2

What is the range of y = 1/x^2?

Question 3

For a bottom-heavy function, the horizontal asymptote is y = _____.

Question 4

CASE STUDY: A company is analyzing the graph of a rational function to determine its domain and range. They need to identify the vertical and horizontal asymptotes to make accurate predictions.

Identify the incorrect asymptote application.

Question 5

CASE STUDY: A student is learning about rational functions and needs to understand how to determine the horizontal asymptote when the degrees of the numerator and denominator are equal.

Select three correct methods for finding horizontal asymptote.

Question 6

A hole in a graph is an infinite discontinuity.

Question 7

How do you find a slant asymptote?

Question 8

The range of y = 1/x excludes y = _____.

Question 9

CASE STUDY: An engineer is tasked with graphing a rational function that has been shifted horizontally and vertically. They need to determine the new asymptotes and graph the function accurately.

Identify the incorrect graphing step.

Question 10

A slant asymptote occurs when numerator's degree is one more than denominator's.

Question 11

How does a negative sign affect a graph?

Question 12

The vertical asymptote of y = 1/x is at x = _____.

Question 13

Horizontal asymptotes depend on the degrees of numerator and denominator.

Question 14

What determines a rational function's vertical asymptote?

Question 15

The domain of y = 1/x excludes x = _____.

Question 16

The range of a function includes horizontal asymptotes.

Question 17

What is the domain of y = 1/x?

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