Understanding Rational Functions and Asymptotes

The video tutorial covers graphing rational functions, focusing on identifying horizontal and vertical asymptotes. It explains how to determine these asymptotes by analyzing the highest degree terms in the numerator and denominator. The tutorial also demonstrates graphing the function and verifying the graph using a calculator, highlighting the behavior of the function as it approaches asymptotes.

What is the horizontal asymptote of the function y = 2x / (x + 1)?

• y = 2

• y = x

• y = 1

• y = 0

Why is the function y = 2x / (x + 1) undefined at x = -1?

• The function is always defined.

• Both numerator and denominator become zero.

• The denominator becomes zero.

• The numerator becomes zero.

In the function y = (x + 1) / (x + 1), what happens at x = -1?

• There is a hole in the graph.

• The function is defined.

• There is a vertical asymptote.

• The function equals zero.

What is the vertical asymptote of the function y = 2x / (x + 1)?

• x = -1

• x = 2

• x = 1

• x = 0

What is the value of y when x = 0 for the function y = 2x / (x + 1)?

• y = 0

• y = -1

• y = 1

• y = 2

What is the value of y when x = 1 for the function y = 2x / (x + 1)?

• y = -1

• y = 2

• y = 1

• y = 0

What is the behavior of the graph as it approaches the vertical asymptote from the right?

• It oscillates.

• It remains constant.

• It approaches negative infinity.

• It approaches positive infinity.

What is the value of y when x = -2 for the function y = 2x / (x + 1)?

• y = 4

• y = -4

• y = -2

• y = 2

What is the value of y when x = -3 for the function y = 2x / (x + 1)?

• y = -6

• y = -3

• y = 3

• y = 6

What does the graphing calculator do when plotting the function y = 2x / (x + 1)?

• It only plots the asymptotes.

• It shows the exact graph.

• It connects all points including asymptotes.

• It ignores the asymptotes.