Exploring Graphing Rational Functions: Part 3 Insights

This video tutorial explains how to graph rational functions by identifying key characteristics such as holes, x and y intercepts, and vertical and horizontal asymptotes. The process begins with factoring the numerator and denominator to find holes, followed by setting equations to find intercepts. The tutorial also covers determining asymptotes based on the degree of the function and graphing the function using these features. The video provides a step-by-step guide to ensure a comprehensive understanding of graphing rational functions.

What are the key characteristics of rational functions that need to be identified for graphing?

• None of the above

• Only vertical and horizontal asymptotes

• Holes, x-intercepts, y-intercepts, vertical and horizontal asymptotes

• Only x-intercepts and y-intercepts

What is the first step in graphing a rational function?

• Factoring the numerator and denominator

• Determining the horizontal asymptote

• Finding the x-intercept

• Plotting the graph

How do you find the x-coordinate of a hole in the graph?

• Set the denominator equal to zero

• Set the numerator equal to zero

• Set the canceled factor equal to zero

• Set the entire function equal to zero

What is the x-intercept of the function y = (x - 1) / (x - 4)?

• (0, -1)

• (0, 1)

• (4, 0)

• (1, 0)

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

• Set the denominator equal to zero

• Set the numerator equal to zero

• Set x equal to zero

• Set y equal to zero

What is the vertical asymptote of the function y = (x - 1) / (x - 4)?

• x = 1

• x = 0

• x = -4

• x = 4

How is the horizontal asymptote determined when the degrees of the numerator and denominator are equal?

• By dividing the leading coefficients

• By setting the denominator equal to zero

• By subtracting the degrees

• By setting the numerator equal to zero

What is the horizontal asymptote of the function y = (x - 1) / (x - 4)?

• y = 0

• y = 1

• y = -1

• y = 4

How is a hole represented on the graph?

• As a solid line

• As an open circle

• As a dashed line

• As a filled circle

What is the coordinate of the point found by evaluating f(5) for the function y = (x - 1) / (x - 4)?

• (5, 1)

• (5, 4)

• (5, -1)

• (5, 0)