Graphing a rational function with a slant asymptote

The video tutorial explains how to graph rational functions by identifying critical points, vertical and horizontal asymptotes, and intercepts. It covers the rules for determining asymptotes, including vertical, horizontal, and slant asymptotes, and demonstrates how to find X and Y intercepts. The tutorial also provides techniques for plotting points and graphing the function while considering the behavior of the graph near asymptotes.

What is the first step in graphing a rational function?

• Find the X-intercept

• Determine the vertical asymptote

• Identify the horizontal asymptote

• Calculate the Y-intercept

Which rule applies when the exponent of the numerator is smaller than the exponent of the denominator?

• The horizontal asymptote is y = 0

• There is no horizontal asymptote

• The horizontal asymptote is y = 1

• The horizontal asymptote is y = 2

What method can be used to find an oblique asymptote?

• Neither synthetic nor long division

• Synthetic division only

• Long division only

• Both synthetic and long division

What happens when you try to find the X-intercept of a function with a zero in the denominator?

• The X-intercept is one

• The X-intercept is undefined

• The X-intercept is negative

• The X-intercept is zero

What is the Y-intercept of a function if the denominator is zero?

• The Y-intercept is one

• The Y-intercept is undefined

• The Y-intercept is negative

• The Y-intercept is zero

How should you plot points when graphing a rational function without a graphing calculator?

• Plot as many points as possible

• Plot no points

• Plot only the intercepts

• Plot only the asymptotes

What is the importance of plotting points on both sides of an asymptote?

• To determine the slope

• To understand the graph's behavior

• To find the exact intercepts

• To calculate the function's value

What should you do if your graph crosses a horizontal or slant asymptote?

• Change the function

• Check the graph's behavior

• Recalculate the asymptote

• Ignore it

What is the slope of the line y = 2x?

• 2

• -2

• 1

• 0

What is the final step in graphing a rational function?

• Calculating the slope

• Connecting the points and asymptotes

• Plotting the points

• Finding the intercepts