Graphing Rational Functions

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9.2 Graphing Simple Rational Functions

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Presentation transcript:

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

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

II. The Rational Function Parent Functions: a: Determines the size and direction 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 h: horizontal shift (Vertical Asymptote: x = #) K: Vertical Shift (Horizontal Asymptote: y = #)

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

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

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

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

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

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

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