Lesson 4: 7-4 Graphing Rational Functions

1. What can a polynomial identity tell you just by looking at it?
2. Can the vertical asymptote cross the y axis?
3. Can the horizontal asymptote cross the x axis?
4. How do you find the zeros of the problem?
5. How do you find the asymptote?

Rational Function
Vertical Asymptote
Horizontal Asymptote
Oblique Asymptote
Point Discontinuity

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

SAT questions related to rational functions: 1-3-13, 6-3-12

A rational function has an equation of the form f(x)=a(x)/b(x), where a(x) and b(x) are polynomial functions and b(x) does not equal 0. Some graphs of rational functions have breaks in continuity.

Regina bought a season pass to a water park for $146. She plans on paying for one meal in the park every time she visits. The park claims that meals on average cost $12.49. The rational function W(m)=(12.49m+146)/m can be used to determine the average cost W(m) for visiting the park m times.

Zeros of rational functions occur at the values that make the numerator equal to zero. Vertical asymptotes occur at the values that make the denominator equal to zero.

Challenge students to explain the rules for finding horizontal and oblique asymptotes. While the chapter shows students how to find them, the explanation of why the rules work can be left to high ability students. Scaffold the task by having students examine graphs of varying degrees in the numerator and denominator and look for general patterns in the asymptotes.

Have students write a list of tips to help someone draw the graphs of rational functions.

McGraw Hill resources

McGraw Hill resources