1. Objectives: 1. Be able to identify the parent function for a rational. 2.Be able list the characteristic of a rational function. 3.Be able to graph rational functions in general form. 4.Be able to graph rational functions in polynomial form. Critical Vocabulary: Parent function, Rational Function, Asymptote

2. I. The Parent Function Parent Functions: This function will have a vertical asymptote at x = 0. This function will have a horizontal asymptote at y = 0. This function will be a hyperbola (which consists of 2 symmetrical parts called branches. Domain: All Real #; except x ≠ 0 Range: All Real #; except y ≠ 0

3. II. The Rational Function Parent Functions: a: Determines the size and direction h: horizontal shift (Vertical Asymptote: x = #) K: Vertical Shift (Horizontal Asymptote: y = #) If a is positive the graph will be in sections 1 and 3. If a is negative the graph will be in sections 2 and 4. lal > 1: Hyperbolas change slower lal < 1: Hyperbolas change quicker

4. III. Graphing a Rational Function (General Form) Example 1: Graph 1 st : List the Characteristics: Hyperbolas in S1 and S3 Slow Change VA: x = -2 HA: y = -3 2 nd : Graph your asymptotes 3 rd : Find Two more points x y 1 -2 -5 -4 4 th : Find the Domain and Range D: All Real #; except x ≠ -2 R: All Real #; except y ≠ -3

5. III. Graphing a Rational Function (General Form) Example 2: Graph 1 st : List the Characteristics: Hyperbolas in S2 and S4 Slow Change VA: x = 1 HA: y = 3 2 nd : Graph your asymptotes 3 rd : Find Two more points x y 5 2 -3 4 4 th : Find the Domain and Range D: All Real #; except x ≠ 1 R: All Real #; except y ≠ 3

6. Page 561 #12, 13, 19, 21 a.List the Characteristics b.Graph (show table) c.Find Domain and Range

7. Objectives: 1. Be able to identify the parent function for a rational. 2.Be able list the characteristic of a rational function. 3.Be able to graph rational functions in general form. 4.Be able to graph rational functions in polynomial form. Critical Vocabulary: Parent function, Rational Function, Asymptote Warm Up: Graph the following:

8. IV. Graphing a Rational Function (Polynomial Form) Example 1: Graph 1 st : Find (and graph) your asymptotes 3 rd : Find Two more points x y 4 9 2 -5 4 th : Find the Domain and Range D: All Real #; except x ≠ 3 R: All Real #; except y ≠ 2 VA: Place where the function is und. x - 3 = 0x = 3 HA: Leading co-efficient of numerator divided by the leading co-efficient of the denominator. y = 2

9. IV. Graphing a Rational Function (Polynomial Form) Example 2: Graph 1 st : Find (and graph) your asymptotes 3 rd : Find Two more points x y 0 -3 -4 9 4 th : Find the Domain and Range D: All Real #; except x ≠ -2 R: All Real #; except y ≠ 3 VA: Place where the function is und. x + 2 = 0x = -2 HA: Leading co-efficient of numerator divided by the leading co-efficient of the denominator. y = 3

10. Page 562 #27, 28, 30 (3 problems)