Domains and Graphs of Rational Functions: Lesson 30

LESSON OBJECTIVES: 1.Create rational functions to model situations. 2.Analyze graphs of rational functions and their asymptotes.

1)Direct Variation: A linear function in the form y = kx, where k 0. 2)Constant: A linear function in the form y = b. 3)Identity: A linear function in the form y = x. 4)Absolute Value: A function in the form y = |mx + b| + c (m 0).

5)Greatest Integer: A function in the form y = [x]. 6)Rational Function: A function that is the ratio of two polynomials. The polynomial you are dividing by cannot be zero. A function in the form y = (x + 3)(x – 5) (x – 3)

11)Continuity: Can be traced with a pencil never leaving the paper. 12)Vertical Asymptotes: x = 3. Function grows to infinity. 13)Horizontal Asymptotes: y = 8. Function approaches as x tends to plus or minus infinity.

Direct Variation: A linear function in the form y = kx, where k 0.

Constant: A linear function in the form y = b. y = 3

Identity: A linear function in the form y = x.

Absolute Value: A function in the form y = |mx + b| + c (m 0).

Greatest Integer: A function in the form y = [x].

Rational Function: A function that is the ratio of two polynomials.

Vertical and Horizontal Asymptotes

Study the graph handout of the rational function and describe the pattern of change in function values as approaches 3. The graph has = -1 and = 3 as vertical asymptotes. As values of approach -1 from below, the graph suggests that values of f() decrease without lower bound.

As values of approach -1 from above, the graph suggests that values of f() increase without upper bound. As values of approach 3 from below 3, the function values decrease rapidly approaching negative infinity. As values of approach 3 from above 3, the function values approach positive infinity.

HOMEWORK!! 1)“Graphing Rational Functions” Worksheet. 2)“Domains and Graphs of Rational Functions” Worksheet.