Rational Functions and Asymptotes

The video tutorial explains how to graph a rational function by first identifying and plotting asymptotes. It emphasizes the importance of simplifying the function through factoring to correctly identify vertical asymptotes. The tutorial then demonstrates how to plot points to understand the graph's shape and highlights the significance of recognizing holes in the graph, which occur when factors cancel out in the original function.

What is the first step in graphing a rational function?

• Calculating the slope

• Plotting the x-intercepts

• Identifying the asymptotes

• Finding the y-intercept

Where do vertical asymptotes occur in a rational function?

• Where the function is undefined

• Where the denominator is zero

• Where both numerator and denominator are zero

• Where the numerator is zero

What should be done before identifying vertical asymptotes?

• Find the x-intercepts

• Simplify the rational function

• Calculate the derivative

• Determine the range

What is the vertical asymptote of the simplified function in the video?

• x = 4

• x = -2

• x = 0

• x = 2

What is the horizontal asymptote of the function after simplification?

• y = 0

• y = 1

• y = -1

• y = 2

What is the value of the function at x = 0?

• 1

• 0

• 2

• -1

What is the value of the function at x = 1?

• 2

• 1

• 0

• -2

What is the value of the function at x = -1?

• -2/3

• 2/3

• -1

• 1

What happens to the graph as it approaches the asymptotes?

• It intersects the asymptotes

• It becomes undefined

• It approaches but never touches the asymptotes

• It oscillates around the asymptotes

What is the value of the function at x = 3?

• 2

• -2

• 0

• 1