Asymptotic Behavior of Rational Functions

The video tutorial explains how to use arrow notation to describe the local and end behavior of rational functions. It covers identifying vertical and horizontal asymptotes and analyzing the behavior of the function as it approaches these asymptotes. The tutorial provides a step-by-step guide to understanding how the function behaves as x approaches positive and negative infinity and as it nears the vertical asymptote from both sides. The video concludes with a verification of the analysis, ensuring the correct understanding of the function's behavior.

What is the vertical asymptote of the given rational function?

• y = -2

• y = -1

• x = -2

• x = -1

What is the horizontal asymptote of the given rational function?

• y = -2

• y = -1

• x = -2

• x = -1

As x approaches negative infinity, what does y approach?

• Negative one

• Zero

• Positive infinity

• Negative infinity

What happens to y as x approaches positive infinity?

• Y approaches zero

• Y approaches negative one

• Y approaches negative infinity

• Y approaches positive infinity

As x approaches the vertical asymptote from the left, what does y approach?

• Positive infinity

• Negative infinity

• Zero

• Negative one

What happens to y as x approaches the vertical asymptote from the right?

• Y approaches negative infinity

• Y approaches negative one

• Y approaches zero

• Y approaches positive infinity

Which of the following is true about the end behavior of the function?

• Y approaches zero as x approaches positive infinity

• Y approaches negative one as x approaches positive infinity

• Y approaches negative infinity as x approaches negative infinity

• Y approaches positive infinity as x approaches negative infinity

Which behavior is observed as x approaches the vertical asymptote from the left?

• Y approaches zero

• Y approaches negative infinity

• Y approaches positive infinity

• Y approaches negative one

Which behavior is observed as x approaches the vertical asymptote from the right?

• Y approaches zero

• Y approaches positive infinity

• Y approaches negative infinity

• Y approaches negative one

How many behaviors were identified in the video?

• Four

• Three

• Two

• Five