8.2: Graph Simple Rational Functions

Slides:

Advertisements

Similar presentations

A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = . Its graph is a.

Advertisements

Rational Functions 8-4 Warm Up Lesson Presentation Lesson Quiz

Rational Functions Sec. 2.7a. Definition: Rational Functions Let f and g be polynomial functions with g (x ) = 0. Then the function given by is a rational.

RATIONAL FUNCTIONS 2.6. RATIONAL FUNCTIONS VERTICAL ASYMPTOTES  To find vertical asymptotes first reduce the function if possible.  Set the denominator.

2.7 – Graphs of Rational Functions. By then end of today you will learn about……. Rational Functions Transformations of the Reciprocal function Limits.

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

3.6 Graph Rational Functions Part II. Remember Rational functions have asymptotes To find the vertical asymptote, set the denominator = 0 and solve for.

Rational Functions 4-2.

3.7 Graphing Rational Functions Obj: graph rational functions with asymptotes and holes and evaluate limits of rational functions.

Lesson 2.6 Read: Pages Page 152: #1-37 (EOO), 47, 49, 51.

A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = . Its graph is a.

Asymptotes Objective: -Be able to find vertical and horizontal asymptotes.

Chapter 7 Polynomial and Rational Functions with Applications Section 7.2.

Rational Functions and Their Graphs

Graphing Rational Functions

Key Information Starting Last Unit Today –Graphing –Factoring –Solving Equations –Common Denominators –Domain and Range (Interval Notation) Factoring will.

Rational Functions and Asymptotes

Find the zeros of each function.

Rational Functions and Their Graphs Objectives Find the domain of rational functions. Find horizontal and vertical asymptotes of graphs of rational functions.

November 1 st copyright2009merrydavidson Warm Up 1) Complete the Square to change to Standard Form. f(x) = 2x 2 – 8x + 9 2)Find ALL roots using the rational.

What is the end behavior?

Essential Question: How do you find intercepts, vertical asymptotes, horizontal asymptotes and holes? Students will write a summary describing the different.

Lesson 8-3: Graphing Rational Functions

Academy Algebra II/Trig 5.2: Graph Simple Rational Functions.

Calculus Section 2.5 Find infinite limits of functions Given the function f(x) = Find =  Note: The line x = 0 is a vertical asymptote.

Holt McDougal Algebra 2 Rational Functions Graph rational functions. Transform rational functions by changing parameters. Objectives.

Transformations of Functions (Chapter 2.3-page 97)

The base e P 667. Essential Question How is the graph of g(x) = ae x – h + k related to the graph of f(x) = e x.

Calculus Section 2.5 Find infinite limits of functions Given the function f(x) = Find =  Note: The line x = 0 is a vertical asymptote.

A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = . Its graph is a.

Chapter Rational Function. Objectives Graph rational functions. Transform rational functions by changing parameters.

Rational Functions and Models

Characteristics of Rational Functions

Section 2.6 Rational Functions Part 2

Rational Functions and Asymptotes (Section 2-6)

8.2 Rational Functions and Their Graphs

Calculus section 1.1 – 1.4 Review algebraic concepts

Rational Functions and Their Graphs

Section 3.5 Rational Functions and Their Graphs

4.4 Rational Functions Objectives:

1.2A Stretches The graph of y + 3 = f(x) is the graph of f(x) translated…  up 3 units  left 3 units  down 3 units  right 3 units x 2. The.

Graphing more challenging Rational Functions

Graphing Rational Functions

2.7 Graphs of Rational Functions

The Parent Function can be transformed by using

Rational Functions, Transformations

Rational Functions and Asymptotes

7.1 & Graphing Exponential Transformations

Worksheet Key 1/1/2019 8:06 AM 6.2: Square Root Graphs.

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

Grade Distribution 2nd 5th A 8 9 B 6 7 C 3 D 2 1 F 100+ Range

Section 5.2 – Logarithmic Functions

Graphing Rational Functions

Graphing Simple Rational Functions p 381

Graph rational functions.

A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = . Its graph is a.

SQUARE ROOT Functions 4/6/2019 4:09 PM 8-7: Square Root Graphs.

SQUARE ROOT Functions Radical functions

2.7 Graphs of Rational Functions

27 – Graphing Rational Functions No Calculator

Rational Functions Section 8.3.

Rational Functions Section 8.3 Day 2.

19A-19E Cubic, Quartic, and Rational Functions

Section 8.4 – Graphing Rational Functions

Warm- up For each find the transformation, domain, range, End Behavior and Increasing and Decreasing Interval. 1. y=(x+3) y = log x y.

Domain of Rational Functions

Exponential Functions and Their Graphs

Warm-up: Solve each equation for a. 1. 2a–b = 3c

Warm up honors algebra 2 3/1/19

Presentation transcript:

8.2: Graph Simple Rational Functions Grade Distribution 1st 4th 7th 9th A B C D F No Shows 100+ Range Avg 8.2: Graph Simple Rational Functions 2/23/2019 10:24 PM

Graphing Simple Rational Functions Section 8.2

8.2: Graph Simple Rational Functions The rational function f(x) = 1/x can be transformed by using methods similar to those used to transform other types of functions. 8.2: Graph Simple Rational Functions 2/23/2019 10:24 PM

8.2: Graph Simple Rational Functions 2/23/2019 10:24 PM

Domain and Range The domain is found by making the denominator equal to zero. It is what the restrictions are. Then, set the denominator equal to zero and solve for x. The range is found by establishing the y-intercept of the graph In Interval Notation, the domain and range will be from (–∞, x) U (x, ∞) where x represents any holes or vertical asymptotes. 4.4: Rational Functions 2/23/2019 10:24 PM

Example 1 Using the graph of f(x) = 1/x as a guide, describe the transformation, graph each function, and determine the domain and range of g(x) = (1/x) – 3 in Interval Notation. If k = –3, translate 3 units down. 8.2: Graph Simple Rational Functions 2/23/2019 10:24 PM

Example 2 Using the graph of f(x) = 1/x as a guide, describe the transformation, graph each function, and determine the domain and range of g(x) = (1/(x + 2)) If h = –2, translate 2 units left. 8.2: Graph Simple Rational Functions 2/23/2019 10:24 PM

Example 3 Using the graph of f(x) = 1/x as a guide, describe the transformation, graph each function, and determine the domain and range of g(x) = (–4/(x + 2)) – 1 If k = –1, translate 1 units down. If h = 2, translate 2 units left. If a = –4, translate 2 units left. 8.2: Graph Simple Rational Functions 2/23/2019 10:24 PM

8.2: Graph Simple Rational Functions Your Turn Using the graph of f(x) = 1/x as a guide, describe the transformation, graph each function, and determine the domain and range of g(x) = (1/(x – 3)) + 2 8.2: Graph Simple Rational Functions 2/23/2019 10:24 PM

8.2: Graph Simple Rational Functions Assignment Page 561 11-23 ALL: DO NOT GRAPH; Label the domain and range of each function. 8.2: Graph Simple Rational Functions 2/23/2019 10:24 PM