Graphing a rational function with no horizontal asymptote

The video tutorial explains how to graph a function by identifying vertical and horizontal asymptotes, finding x- and y-intercepts, and plotting points. It emphasizes the importance of understanding the behavior of the graph near asymptotes and using a graphing calculator for accuracy.

What is the condition for a vertical asymptote in a rational function?

• When the function equals one

• When the numerator equals zero

• When both numerator and denominator equal zero

• When the denominator equals zero

If the degree of the numerator is greater than the degree of the denominator, what can be said about the horizontal asymptote?

• The horizontal asymptote is at y = 0

• There is one horizontal asymptote

• There are two horizontal asymptotes

• There are no horizontal asymptotes

How do you find the x-intercept of a rational function?

• Set the numerator equal to zero

• Set the denominator equal to zero

• Set both numerator and denominator equal to zero

• Set the function equal to one

What is the y-intercept of a function if f(x) = (x + 1)^3 / (x + 2)^2?

• 2

• 1

• 1/2

• 1/4

Why is it important to plot additional points on the graph of a rational function?

• To determine the function's domain

• To find the exact shape of the graph

• To verify the function's range

• To ensure the graph approaches the asymptotes correctly

What should you do if you cannot evaluate the function at a certain point due to a vertical asymptote?

• Choose points far from the asymptote

• Choose points very close to the asymptote

• Ignore the point

• Use the same point on the opposite side of the graph

What is the role of a graphing calculator in plotting rational functions?

• To find the exact intercepts

• To verify the plotted points and asymptotes

• To calculate the function's domain

• To determine the function's range