Graph 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

9.3 Rational Functions and Their Graphs

Functions AII.7 e Objectives: Find the Vertical Asymptotes Find the Horizontal Asymptotes.

Rational Expressions, Vertical Asymptotes, and Holes.

Graphs of Exponential and Logarithmic Functions

Rational Functions 8-4 Warm Up Lesson Presentation Lesson Quiz

Section 5.2 – Properties of Rational Functions

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

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

ACT Class Openers:

3.6 Warm Up Find the initial point, state the domain & range, and compare to the parent function f(x) = √x. y = 3√x – 1 y = -1/2√x y = - √(x-1) + 2.

Rational Functions. 5 values to consider 1)Domain 2)Horizontal Asymptotes 3)Vertical Asymptotes 4)Holes 5)Zeros.

Rational Functions 4-2.

9.3 Rational Functions and Their Graphs Rational Function – A function that is written as, where P(x) and Q(x) are polynomial functions. The domain of.

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.

RATIONAL FUNCTIONS Graphing The Rational Parent Function’s Equation and Graph: The Rational Parent Function’s Equation and Graph:. The graph splits.

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

Graphing Rational Functions

What is the symmetry? f(x)= x 3 –x.

Rational Functions and Asymptotes

Find the zeros of each function.

What is the end behavior?

I can graph a rational function.

Objective: Students will be able to graph rational functions using their asymptotes and zeros.

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

Holt McDougal Algebra 2 Rational Functions Holt Algebra 2Holt McDougal Algebra 2 How do we graph rational functions? How do we transform 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.

9.3 Graphing Rational Functions What is rational function? What is an asymptote? Which ones can possibly be crossed? A function that is written in fractional.

Graphing Rational Expressions. Find the domain: Graph it:

Check It Out! Example 2 Identify the asymptotes, domain, and range of the function g(x) = – 5. Vertical asymptote: x = 3 Domain: {x|x ≠ 3} Horizontal asymptote:

Lesson 21 Finding holes and asymptotes Lesson 21 February 21, 2013.

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.

Holt Algebra Rational Functions The values of h and k affect the locations of the asymptotes, the domain, and the range of rational functions whose.

8.2 The Reciprocal Function Family Honors. The Reciprocal Functions The Reciprocal function f(x) = x ≠0 D: {x|x ≠ 0} R: {y|y ≠ 0} Va: x = 0 Ha: y = 0.

Rational Functions A rational function has the form

Rational Functions…… and their Graphs

4.4 Rational Functions A Rational Function is a function whose rule is the quotient of two polynomials. i.e. f(x) = 1

Rational Functions and Asymptotes (Section 2-6)

Graphing Rational Functions

8.2 Rational Functions and Their Graphs

28 – The Slant Asymptote No Calculator

Rational functions are quotients of polynomial functions.

Rational Functions and Their Graphs

Section 3.5 Rational Functions and Their Graphs

4.4 Rational Functions Objectives:

26 – Limits and Continuity II – Day 2 No Calculator

Graphing Rational Functions

The Parent Function can be transformed by using

MATH 1310 Section 5.1.

Rational Functions, Transformations

Graphing Rational Functions

MATH 1310 Section 4.4.

Graphing Rational Functions

Simplifying rational expressions

2.6 Section 2.6.

8.2: Graph Simple 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.

Graphing Rational Expressions

Warm Up – 12/4 - Wednesday Rationalize: − 5.

MATH 1310 Section 5.1.

Rational Functions A rational function f(x) is a function that can be written as where p(x) and q(x) are polynomial functions and q(x) 0 . A rational.

EQ: What other functions can be made from

MATH 1310 Section 5.1.

Find the zeros of each function.

MATH 1310 Section 4.4.

Presentation transcript:

x -4 -2 -1 -½ ½ 1 2 4 8-4 LEARNING GOALS 8.4.1 Graph rational functions. 8.4.2 Transform rational functions by changing parameters. 8.4.3 Identify vertical and horizontal asymptotes, and holes The parent function for the family of rational functions is: Its graph is called a _______________. They are characterized by two separate branches and two asymptotes. Domain: Range: x -4 -2 -1 -½ ½ 1 2 4 A _____________________ function is a function whose graph has one or more gaps or breaks. Example: Hyperbolas A _____________________ function is a function whose graph has no gaps or breaks. Examples: Lines, Parabolas, Logarithmic Curves, Exponential Functions 8.4 Pg. 1

Example 1: Transforming Rational Functions Using the graph of as a guide, describe the transformation and graph each function. A. B. 8.4 Pg. 2

Example 2: Determining Properties of Hyperbolas Using the graph of as a guide, describe the transformation and graph each function. C. Example 2: Determining Properties of Hyperbolas A. Identify the asymptotes, domain, and range of the function Sketch the graph: Vertical asymptote: Domain: Horizontal asymptote: Range: 8.4 Pg. 3

ZEROS B. Identify the asymptotes, domain, and range of the function Vertical asymptote: Sketch the graph: Domain: Horizontal asymptote: Range: C. Identify the asymptotes, domain, and range of the function Vertical asymptote: Sketch the graph: Domain: Horizontal asymptote: Range: ZEROS What is a “zero”? What does it look like graphically? What has to be true about a fraction to make it = 0 Example 3: Finding Zeros Identify the zeros of f(x). A. B. 8.4 Pg. 4

Example 3 Continued: Finding Asymptotes Vertical asymptotes are written as: X = _____ They are found by factoring the denominator and setting it equal to zero. Horizontal asymptotes are written as: Y = ______ They are found by looking at the degree of the numerator and denominator using the chart below. Degree of numerator & denominator N > D N < D N = D Type of horizontal asymptote None y = 0 y = Identify both the vertical and horizontal asymptotes of the function. A. B. C. D. 8.4 Pg. 5

Example 4: Graphing Rational Functions with Holes When a functions numerator = ____ and denominator = ____ for the same x value the graph may have a ____________. HOLE: NO HOLE: Example 4: Graphing Rational Functions with Holes Identify holes in the graph of f(x). Then graph. A. B. 8.4 Pg. 6