1 / 10

Objectives: 1. Be able to identify the parent function for a rational.

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:

hollye
Download Presentation

Objectives: 1. Be able to identify the parent function for a rational.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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

  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 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 = #)

  4. 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 1 -5 -2 -4 D: All Real #; except x ≠ -2 R: All Real #; except y ≠ -3 4th: Find the Domain and Range

  5. 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 5 -3 2 4 D: All Real #; except x ≠ 1 R: All Real #; except y ≠ 3 4th: Find the Domain and Range

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

  7. 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:

  8. 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 4 2 9 -5 D: All Real #; except x ≠ 3 R: All Real #; except y ≠ 2 4th: Find the Domain and Range

  9. 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 0 -4 -3 9 D: All Real #; except x ≠ -2 R: All Real #; except y ≠ 3 4th: Find the Domain and Range

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

More Related