Graph without a Vertical Asymptote No Vertical Asymptote

The video tutorial addresses common challenges students face when graphing rational expressions. It covers the importance of simplification, identifying vertical and horizontal asymptotes, and finding intercepts. The instructor explains why imaginary numbers cannot be used for vertical asymptotes and clarifies the difference between vertical and horizontal asymptotes. The video also demonstrates how to determine the shape of a graph using test points and provides additional resources for further learning.

What is the first step in graphing a rational expression according to the video?

• Identify the x-intercepts

• Simplify the expression

• Find the horizontal asymptotes

• Plot the graph directly

Why is there no vertical asymptote in the given expression?

• The denominator is zero

• The numerator is zero

• The expression is not simplified

• The solutions are imaginary

How do you determine the horizontal asymptote of a rational expression?

• By finding the x-intercepts

• By comparing the degrees of the numerator and denominator

• By simplifying the expression

• By setting the numerator equal to zero

What is the x-intercept of the expression discussed in the video?

• x = 2

• x = 5

• x = 0

• x = -2

What is the purpose of using test points when graphing a rational expression?

• To find the vertical asymptotes

• To determine the horizontal asymptotes

• To simplify the expression

• To verify the graph's shape