Rational Functions II: Analyzing Graphs

Slides:

Advertisements

Similar presentations

Polynomial Inequalities in One Variable

Advertisements

Checking an equation for symmetry

9.3 Rational Functions and Their Graphs

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 Functions I; Rational Functions II – Analyzing Graphs

Rational function A function  of the form where p(x) and q(x) are polynomials, with q(x) ≠ 0, is called a rational function.

Math 139 – The Graph of a Rational Function 3 examples General Steps to Graph a Rational Function 1) Factor the numerator and the denominator 2) State.

Rational Functions Find the Domain of a function

Objectives: Find the domain of a Rational Function Determine the Vertical Asymptotes of a Rational Function Determine the Horizontal or Oblique Asymptotes.

EXAMPLE 1 Graph a rational function (m < n) Graph y =. State the domain and range. 6 x SOLUTION The degree of the numerator, 0, is less than the.

Section4.2 Rational Functions and Their Graphs. Rational Functions.

5.3 Graphs of Rational Functions

5.3 Graphs of Rational Functions

Analyzing Polynomial & Rational Functions & Their Graphs Steps in Analysis of Graphs of Poly-Rat Functions 1)Examine graph for the domain with attention.

Sullivan PreCalculus Section 3

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Section 4.1 Polynomial Functions. A polynomial function is a function of the form a n, a n-1,…, a 1, a 0 are real numbers n is a nonnegative integer D:

9.3 Graphing Rational Functions Algebra II w/ trig.

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

Rational Functions Intro - Chapter 4.4.  Let x = ___ to find y – intercepts A rational function is the _______ of two polynomials RATIO Graphs of Rational.

Curve sketching This PowerPoint presentation shows the different stages involved in sketching the graph.

Sullivan Algebra and Trigonometry: Section 4.4 Rational Functions II: Analyzing Graphs Objectives Analyze the Graph of a Rational Function.

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 3 Polynomial and Rational Functions.

Chapter 3 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Rational Functions and Their Graphs.

1 Analyze and sketch graphs of rational functions. 2.6 What You Should Learn.

Rational Functions Marvin Marvin Pre-cal Pre-cal.

Rational Functions A rational function has the form

Rational Functions and Models

Polynomial Functions Objectives: Identify Polynomials and their Degree

Section 2.6 Rational Functions Part 2

Rational Functions.

4.4 Rational Functions II: Analyzing Graphs

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

GRAPHING RATIONAL FUNCTIONS

Rational Functions (Algebraic Fractions)

Rational functions are quotients of polynomial functions.

Section 5.3 – The Graph of a Rational Function

Summary Curve Sketching

Graphs of Equations In Two Variables; Intercepts; Symmetry

Lesson 2.7 Graphs of Rational Functions

4.4 Rational Functions II: Analyzing Graphs

Section 3.5 Rational Functions and Their Graphs

Guidelines for sketching the graph of a function

Linear Equations in two variables

Graphing Rational Functions

Graphing more challenging Rational Functions

3.5 Rational Functions II: Analyzing Graphs

Asymptotes Rise Their Lovely Heads

“Onions have layers.”.

Rational Functions and Asymptotes

Sec 4.5: Curve Sketching Asymptotes Horizontal Vertical

Notes Over 9.3 Graphing a Rational Function (m < n)

3.5 Rational Functions II: Analyzing Graphs

Graphing Rational Functions

Graphs of Equations Objectives: Find intercepts from a Graph

Chapter 4: Rational, Power, and Root Functions

2.6 Section 2.6.

3.4 Rational Functions I.

Chapter 4: Rational, Power, and Root Functions

“Onions have layers.”.

Section 8.4 – Graphing Rational Functions

Graphs of Equations Objectives: Find intercepts from a Graph

3.5 Rational Functions II: Analyzing Graphs

The Graph of a Rational Function

The Graph of a Rational Function

4.3 Rational Functions I.

Properties of Rational Functions The Graph of a Rational Function

Presentation transcript:

Rational Functions II: Analyzing Graphs Objectives: Analyze the Graph of a Rational Function Solve Applied Problems involving Rational Functions

Analyzing the Graph of a Rational Function 1. Find the domain of the Rational Function 2. Locate the intercepts, if any, of the graph. The x-intercepts, if any, are numbers in the domain that satisfy the equation The y-intercept, if there is one, is 3. Test for symmetry. Replace . If there is symmetry with respect to the y-axis. If there is symmetry with respect to the origin. 4. Write in lowest terms and find the real zeros of the denominator. With in lowest term, each zero will give rise to a vertical asymptote. 5. Locate the horizontal or oblique asymptotes, if any, using the procedure given earlier. Determine points, if any, at which the graph of intersects these asymptotes. 6. Determine where the graph is above the x-axis and where the graph is below the x-axis using the zeros of the numerator and the denominator to divide the x-axis into intervals. 7. Graph the asymptotes, if any, found in steps 4 and 5. Plot the points found in steps 2,5 and 6. Use all the information to connect the points and graph

EX: Graph the rational function 1.

EX: Graph the rational function 2.

EX: Graph the rational function 3.

EX: Graph the rational equation 4.