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Chapter 2 Polynomial and Rational Functions 2.1 Quadratic Functions Definition of a polynomial function Let n be a nonnegative integer so n={0,1,2,3 }

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Chapter 2 Polynomial and Rational Functions 2.1 Quadratic Functions Definition of a polynomial function Let n be a nonnegative integer so n={0,1,2,3 }

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Rational Functions 4-2

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Title: QUADRATIC FUNCTIONS Author: San Juan College Last modified by: rabuckv Created Date: 5/28/1995 4:29:18 PM Document presentation format: On-screen Show

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No vertical asymptotes H.A.: y = 3 Guided Practice Find the horizontal and vertical asymptotes of the given function. Use limits to describe the corresponding behavior.

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If the numerator is a larger degree than the denominator The equation of the asymptote ... Step One: Find the domain of the rational function ... Rational Functions ...

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Horizontal asymptote: y = 2. Check Graph the function on a ... x = 1. As a result, the graph of the function has a vertical asymptote at the line x = 1. ...

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Rational Functions Rational Functions ... of each term and not the variables Example Practice Multiplying/Dividing ... still apply when working with rational expressions!

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Evaluation of Radicals and Rational Functions

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Title: Rational Functions Author: E Gonzalez Last modified by: egonzalez Created Date: 6/10/2001 4:43:47 PM Document presentation format: On-screen Show (4:3)

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section 3.2 rational functions rational functions rational functions take on the form: examples: domain of rational functions any value which zeros out the ...

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Let's Translate. Recall what happens to the graph of a function when we ... Translate ... Page 615: 1, 3, 8, 12 (Make sketches now, no graph paper needed until HW) ...

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... then the vertical line x = a is a vertical asymptote of the rational function ... The LCD is the least common multiple of the denominators. ...

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Determine the vertical asymptotes (if any) of a rational function. ... vertical asymptotes, and horizontal asymptotes for ... Find the slant asymptote for ...

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Rational Functions In this chapter you should Learn to use inverse variation and the graphs of inverse variations to solve real-world problems.

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quotient of two polynomials is called a rational expression. ... shows up as an asymptote. An. asymptote is a line that a. curve approaches but never ...

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On June 4 1996 the first flight. of the ... Banking bugs. Software bugs caused the bank accounts of 823customers of a ... have bugs? Programming errors ...

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Graphing Rational Functions Graph the Rational Function Step II: Graph using the information you found in Step I Ex 1. Graph the Rational Function Step II: Graph ...

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1.8 - Rational Functions MCB4U - Santowski

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UNIT 4: rational functions 8-3 Graphing Rational functions Rational Functions Define Rational Function: is a function with two polynomials (one in the numerator ...

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Chapter 7 Polynomial and Rational Functions with Applications Section 7.1

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Section 2.6 Rational Functions and Asymptotes A rational function is a function written in the form of a polynomial divided by a polynomial. Domain: is the x-values ...

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Graphing Rational Functions

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Most Rational Functions have a vertical asymptote. ... Determine the equations of any vertical asymptotes and the values of x for any ...

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Polynomial and Rational Functions Chapter 3 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA Quadratic Functions and Models ...

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Polynomial and Rational Functions

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We want to graph this rational function showing all relevant characteristics. ... Numerator: Factor out a GCF of x2. Denominator: Factor as a perfect square trinomial. ...

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5.3 Rational Functions and Models ... The speed of a car (in mph) after t seconds is given by: f(t) = .005t3 0.21t2 1.31t 49 ...

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Graphing General Rational Functions p. 547 Steps to graphing rational functions Find the y-intercept. ... State domain & range. 2. x-intercepts: x=0 3.

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8.2 Graph Simple Rational Functions Rational Function A function of the form where p(x) & q(x) are polynomials and q(x) 0. Hyperbola A type of rational function.

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8.1 Inverse Variation: y = k/x. Direct Variation: y = kx ... Use your equation to find the average life span of a lion (heart rate 76 beats/min. ...

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Lesson 2-7: Graphing Rational Functions Advanced Math Topics Definitions Continuity: a graph that is able to be traced without picking up the pencil Asymptote: a line ...

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9.3 Graphing General Rational Functions p. 547 Steps to graphing rational functions Find the y-intercept. Find the x-intercepts. Find vertical asymptote(s).

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Unit 4 Rational functions 8-6 Solving rational expressions Solving Rational Equations To solve a rational equation first multiply each side by the LCD.

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Chapter 7: Rational Equations, Expressions, and Functions 7.1 Multiplication and Division 7.2 Addition and Subtraction 7.3 Division of Polynomials

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oblique asymptote vertical asymptote Oblique Asymptotes To find the equation of an oblique asymptote, ...

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slant asymptotes degree of denom is 1 or higher & numerator is exactly 1 more ... otherwise it's a vertical asymptote. Look at degree of num & denom. ...

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Here I only plotted one more point at x=2 since a point hadn't been plotted to ... For the section between the V.A.'s, we use that it can't cross the H.A. ...

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Hence, there are no intersections between the graph of f(x) and the H.A. ... Here I only plotted one more point at x=-1 since a point hadn't been plotted to ...

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If the y values approach a real number b, then b is the horizontal asymptote. ... The quotient from long division will give the equation for the oblique asymptote. ...

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7. Graph the function on the calculator. 8. Use the results above to graph the equation by hand. ... Simplify the terms and then factor. Draw a number line. ...

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... we see that there is a vertical asymptote at x = 2 because the graph approaches ... see that y = 0 is a horizontal asymptote of the function since y tends to go ...

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Any values of x that are not in the domain of the function but are not V.A. ... of the hole, plug 0 into the reduced form. Graphing Rational Functions ...

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Rational functions: Distance, rate, and time Consider the function t(r) = time required to cover distance of 300 miles at a rate of r mph As rate increases, time ...

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Chapter 6 Rational Expressions, Functions, and Equations 6.1 Rational Expressions and Functions: Multiplying and Dividing Blitzer, Intermediate Algebra, 5e ...

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A polynomial function of degree n, where n is a nonnegative integer, is a ... f(x) = ax2 bx c, where a, b, and c are real numbers with a 0. ...

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Title: 9.3 Rational Functions and Their Graphs Author: home Last modified by: garciak Created Date: 3/25/2006 3:43:14 PM Document presentation format

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Polynomial, Power, and Rational Functions. Chapter 2. Linear and ... Superimpose the graph of the regression model on the scatter plot, and observe the fit. ...

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Sullivan Algebra and Trigonometry: Section 4.3 Rational Functions I Objectives Find the Domain of a Rational Function Determine the Vertical Asymptotes of a Rational ...

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Title: Radical Functions and Rational Exponents Author: MSHS Last modified by: HP Authorized Customer Created Date: 8/10/2004 8:30:57 PM Document presentation format

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9.2 Graphing Simple Rational Functions (p. 540) Rational Function A function of the form where p(x) & q(x) are polynomials and q(x) 0. Hyperbola A type of rational ...

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Rational Functions/Restricted Values. What do we notice? The graph has two branches. Because no point of the graph ... The line is called a VERTICAL ASYMPTOTE. ...

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Chapter 4 Polynomials and Rational Functions 4.1 Polynomial Functions Def: A polynomial in one variable, x, is an expression of the form . The coefficients a0 ...

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Since the domain is , and the vertical asymptotes are x = 2, -1, that means that ... Horizontal asymptotes describe the behavior at the ends of a function. ...

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7-2 Adding and Subtracting Rational Expressions ... the numerator and the denominator are opposites, then the expression equals -1. ...

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... Asymptote ... all holes and vertical asymptotes in each graph. Horizontal Asymptote ... Identify all excluded values, asymptotes, and holes in. the graph of a ...

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