How do you graph a rational function with asymptotes

The video tutorial covers graphing rational functions, focusing on identifying vertical and horizontal asymptotes, and finding x and y-intercepts. It explains the absence of horizontal asymptotes when the degree of the numerator is greater than the denominator. The tutorial also guides on plotting points around the vertical asymptote to sketch the graph accurately, emphasizing the use of graphing calculators for verification.

What is the first step in graphing a rational function?

• Finding the x-intercept

• Identifying the asymptotes

• Calculating the y-intercept

• Plotting random points

How do you determine the vertical asymptote of a rational function?

• Set the numerator equal to zero

• Set the denominator equal to zero

• Calculate the derivative

• Find where the function equals one

What happens when the degree of the numerator is greater than the degree of the denominator?

• There is a horizontal asymptote

• The function is undefined

• There is no horizontal asymptote

• The function has a hole

What is the x-intercept of the function f(x) = x^3 / (x - 1)?

• (0, 1)

• (1, 0)

• (0, 0)

• (1, 1)

How do you find the y-intercept of a function?

• Solve for x

• Set x to zero

• Set y to zero

• Find the derivative

Why is it important to verify points to the left and right of the asymptote?

• To find the maximum value

• To determine the slope

• To ensure the graph is symmetrical

• To confirm the graph's shape

What tool can help visualize the graph of a rational function?

• A ruler

• A graphing calculator

• A protractor

• A compass