Section 2.6 Rational Functions Part 2

Slides:



Advertisements
Similar presentations
9.3 Rational Functions and Their Graphs
Advertisements

3.4 Rational Functions I. A rational function is a function of the form Where p and q are polynomial functions and q is not the zero polynomial. The domain.
Section 5.3 – The Graph of a Rational Function
Rational Expressions GRAPHING.
2.7 Rational Functions and Their Graphs Graphing Rational Functions.
Section 5.2 – Properties of Rational Functions
Homework Check – have homework ready! Learning Goals: Find the Domain of a Rational Function Find the equation of the Vertical and Horizontal Asymptotes.
RATIONAL FUNCTIONS 2.6. RATIONAL FUNCTIONS VERTICAL ASYMPTOTES  To find vertical asymptotes first reduce the function if possible.  Set the denominator.
Objectives: Find the domain of a Rational Function Determine the Vertical Asymptotes of a Rational Function Determine the Horizontal or Oblique Asymptotes.
Section4.2 Rational Functions and Their Graphs. Rational Functions.
ACT Class Opener: om/coord_1213_f016.htm om/coord_1213_f016.htm
Lesson 2.6 Read: Pages Page 152: #1-37 (EOO), 47, 49, 51.
Section 2.6 Rational Functions Part 1
Section 5.2 Properties of Rational Functions
Class Work Find the real zeros by factoring. P(x) = x4 – 2x3 – 8x + 16
Section 3.5 Rational Functions and Their Graphs. Rational Functions.
Section 2.7. Graphs of Rational Functions Slant/Oblique Asymptote: in order for a function to have a slant asymptote the degree of the numerator must.
Rational Functions Intro - Chapter 4.4.  Let x = ___ to find y – intercepts A rational function is the _______ of two polynomials RATIO Graphs of Rational.
Graphing Rational Functions
Sullivan Algebra and Trigonometry: Section 4.4 Rational Functions II: Analyzing Graphs Objectives Analyze the Graph of a Rational Function.
MAT 150 – Class #24 Topics: Graphing Rational Functions Asymptotes Vertical Slanted Horizontals Holes.
C URVE S KETCHING section 3-A continued. Analyzing the graph of a function a)Domain and Range: All real numbers except ___ b)Extrema and the intervals.
Rational Functions and Asymptotes
Graphing Rational Functions Objective: To graph rational functions without a calculator.
A3 3.5a rational functions and domain homework: p odd.
Removable Discontinuities & Vertical Asymptotes
1 Limits at Infinity Section Horizontal Asymptotes The line y = L is a horizontal asymptote of the graph of f if.
2.6 Rational Functions Asymptotes; Can’t touch this stuff Can’t touch this stuff.
1 Analyze and sketch graphs of rational functions. 2.6 What You Should Learn.
2.5 RATIONAL FUNCTIONS DAY 2 Learning Goals – Graphing a rational function with common factors.
I can graph a rational function.
Essential Question: How do you find intercepts, vertical asymptotes, horizontal asymptotes and holes? Students will write a summary describing the different.
MAT 150 – Class #16 Topics: Graphing Rational Functions Asymptotes Vertical Slanted Horizontals Holes.
Lesson 2.7 Page 161: #1-33 (EOO), 43, 47, 59, & 63 EXTRA CREDIT: Pages (Do any 20 problems…You choose ) STUDY: Chapter 2 Exam 10/15 (Make “CHEAT.
CALCULUS CHAPTER 3 SECTION 6: SUMMARY OF CURVE SKETCHING.
Calculus Section 2.5 Find infinite limits of functions Given the function f(x) = Find =  Note: The line x = 0 is a vertical asymptote.
Rational Functions Objective: Finding the domain of a rational function and finding asymptotes.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 2.6 The Graph of a Rational Function.
CHAPTER 9 SECTION 3 RATIONAL FUNCTIONS AND GRAPHS Algebra 2 Notes May 21, 2009.
Notes Over 9.2 Graphing a Rational Function The graph of a has the following characteristics. Horizontal asymptotes: center: Then plot 2 points to the.
Graphing Rational Expressions. Find the domain: Graph it:
Rational Functions. 6 values to consider 1)Domain 2)Horizontal Asymptotes 3)Vertical Asymptotes 4)Holes 5)Zeros 6)Slant Asymptotes.
Calculus Section 2.5 Find infinite limits of functions Given the function f(x) = Find =  Note: The line x = 0 is a vertical asymptote.
Rational Functions A rational function has the form
Warm Up      .
Rational Functions.
Graphs of Rational Functions
8.2 Rational Functions and Their Graphs
Rational functions are quotients of polynomial functions.
Section 5.3 – The Graph of a Rational Function
Rational Functions and Their Graphs
Section 3.5 Rational Functions and Their Graphs
Section 5.4 Limits, Continuity, and Rational Functions
Graphing Rational Functions
Rational Functions and Asymptotes
Section 5.2 – Properties of Rational Functions
Notes Over 9.3 Graphing a Rational Function (m < n)
Factor completely and simplify. State the domain.
Bell Ringer Check your vocabulary….
2.6 Section 2.6.
Graphs of Rational Functions
3.4 Rational Functions I.
The Graph of a Rational Function
The Graph of a Rational Function
Graphing Rational Expressions
Section 3.5 Rational Functions and Their Graphs
4.3 Rational Functions I.
Section 5.4 Limits, Continuity, and Rational Functions
Properties of Rational Functions The Graph of a Rational Function
Presentation transcript:

Section 2.6 Rational Functions Part 2

What you should learn How to analyze and sketch graphs of rational functions How to sketch graphs of rational functions that have slant asymptotes How to use rational functions to model real-life problems

Asymptotes Vertical Horizontal at zeros of the denominator N < D asymptote at y = 0 N = D asymptote at y = aN / aD N > D no Horizontal asymptote

N > D No Horizontal Asymptote Slant Asymptote

2.6 Homework Part 1 Rational Functions page 174 5 - 39 odd,

46. State the domain of the function and identify any vertical and slant asymptotes.