Lesson 8-3: Graphing Rational Functions

Slides:

Advertisements

Similar presentations

Horizontal Vertical Slant and Holes

Advertisements

9.3 Rational Functions and Their Graphs

Ch. 9.3 Rational Functions and Their Graphs

Lesson 8-1: Multiplying and Dividing Rational Expressions

Lesson 8-1: Multiplying and Dividing Rational Expressions

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:

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

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

Sec. 3.7(B) Finding the V.A. , H.A. , X-Intercept, and

Rational Functions & Their Graphs

Solving for the Discontinuities of Rational Equations.

Continuity 2.4.

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.

9.3 Graphing Rational Functions Algebra II w/ trig.

 A asymptote is a line the graph of the function gets closer and closer to but does not touch.

Graphing Rational Functions. 2 xf(x)f(x) xf(x)f(x) As x → 0 –, f(x) → -∞.

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

Lesson 2.6 Rational Functions and Asymptotes. Graph the function: Domain: Range: Increasing/Decreasing: Line that creates a split in the graph:

Warm up: Get 2 color pencils and a ruler Give your best definition and one example of the following: Domain Range Ratio Leading coefficient.

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 A function of the form where p(x) and q(x) are polynomial functions and q(x) ≠ 0. Examples: (MCC9-12.F.IF.7d)

11.2 – Graphing Rational Functions

Pre-Cal Review (Day 2). What is an asymptote? How many different kinds are there?

Rational Functions Standard 4a Find Zeros, Vertical Asymptotes, and Points of Exclusion of a Rational Function and distinguish them from one another.

Lesson 2-7: Graphing Rational Functions

Lesson 2-7: Graphing Rational Functions Advanced Math Topics Mrs. Mongold.

Objective Define and illustrate the use of rational expressions and functions Rational Expressions and Functions Page 532 Rational Expressions and.

Removable Discontinuities & Vertical Asymptotes

I can graph a rational function.

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

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.

Lines that a function approaches but does NOT actually touch.

Rational Functions and their Graphs. Definition Rational Function A rational function f(x) is a function that can be written as where P(x) and Q(x) are.

Graphing Rational Expressions. Find the domain: Graph it:

1 Limits and Continuity. 2 Intro to Continuity As we have seen some graphs have holes in them, some have breaks and some have other irregularities. We.

HW: Handout due at the end of class Wednesday. Do Now: Take out your pencil, notebook, and calculator. 1)Sketch a graph of the following rational function.

Asymptotes of Rational Functions 1/21/2016. Vocab Continuous graph – a graph that has no breaks, jumps, or holes Discontinuous graph – a graph that contains.

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

Graphing Rational Functions Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 xf(x)f(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.

Rational Functions and Asymptotes (Section 2-6)

Graphing Rational Functions

Lesson 1 Notes – Graphing Rational Functions

Graphing Rational Functions

8.2 Rational Functions and Their Graphs

Rational Functions Algebra

Horizontal Vertical Slant and Holes

Section 3.5 Rational Functions and Their Graphs

26 – Limits and Continuity II – Day 2 No Calculator

Graphing Polynomial Functions

Ch 9.1: Graphing Rational Functions

Graphing Rational Functions

Section 7.1 – Rational Expressions

Graphing Rational Functions

Graphing Rational Expressions

26 – Limits and Continuity II – Day 1 No Calculator

Domain, Range, Vertical Asymptotes and Horizontal Asymptotes

Section P.5 – Rational Expressions

Horizontal Vertical Slant and Holes

Rational Functions Section 8.3 Day 2.

Section 8.4 – Graphing Rational Functions

Graphing rational functions

EQ: What other functions can be made from

EQ: How does dividing by zero affect the graph of a function?

Horizontal Vertical Slant and Holes

Ch 9.1: Graphing Rational Functions

Find the zeros of each function.

Presentation transcript:

Lesson 8-3: Graphing Rational Functions

Definitions Continuity: graph may not be able to be traced without picking up pencil Asymptote: a line that the graph of the function approaches, but never touches (this line is graphed as a dotted line) Point discontinuity: a hole in the graph

Vertical Asymptote How to find a Vertical Asymptote: x = the value that makes the rational expression undefined *Set the denominator of the rational expression equal to zero and solve.

Point Discontinuity How to find point discontinuity: * Factor completely * Set any factor that cancels equal to zero and solve. Those are the x values that are points of discontinuity

Graphing Rational Functions f(x) =

Graphing Rational Functions f(x) =

Graphing Rational Functions f(x) =

Graphing Rational Functions f(x)=

Graphing Rational Functions f(x) =

Graphing Rational Functions f(x) =