HOMEWORK: WB p.28-30. RATIONAL FUNCTIONS: GRAPHING.

Slides:



Advertisements
Similar presentations
Rational Expressions, Vertical Asymptotes, and Holes.
Advertisements

Discussion X-intercepts.
Sketching the Graphs of Rational Equations. Consider the equation below: Solve for the discontinuities.
Warm-Up: FACTOR 1.x 2 – x x x 2 – x – 2 5.x 2 – 5x – x 2 – 19x – 5 7.3x x - 8.
2.7 Graphs of Rational Functions. Steps of Graphing 1. Find the domain of the function 2. Simplify the function 3. Find and plot the y-intercept by evaluating.
Graphing Rational Equations (Yeay for Graphing) TS: Demonstrating Understanding of Concepts.
Table of Contents Rational Functions: Horizontal Asymptotes Horizontal Asymptotes: A horizontal asymptote of a rational function is a horizontal line (equation:
Section4.2 Rational Functions and Their Graphs. Rational Functions.
5.3 Graphs of Rational Functions
Table of Contents Graphing Quadratic Functions – Concept A simple quadratic function is given by The graph of a quadratic function in called a parabola.
3.1 – Graphing Linear Equations. Linear equation.
ACT Class Opener: om/coord_1213_f016.htm om/coord_1213_f016.htm
Jeff Bivin -- LZHS Graphing Rational Functions Jeffrey Bivin Lake Zurich High School Last Updated: February 18, 2008.
3 Polynomial and Rational Functions © 2008 Pearson Addison-Wesley. All rights reserved Sections 3.5–3.6.
3.2 – Solving Linear Equations by Graphing. Ex.1 Solve the equation by graphing. x – y = 1.
Rational Parent Function Rational Standard Form Example:Example: Transformations: VA: HA: Domain: Range: Y-intercepts: Roots (x-int): VA: HA: Domain: Range:
Sec. 3.7(B) Finding the V.A. , H.A. , X-Intercept, and
Identifying Features of Linear and Exponential Functions S tandard: A.F.IF.4 Essential Question: How do I identify key features from a graph of a linear.
Graphing Rational Functions Example #6 End ShowEnd Show Slide #1 NextNext We want to graph this rational function showing all relevant characteristics.
Sketching the Graphs of Rational Equations. Consider the equation below: Solve for the discontinuities.
Introduction to Rational Equations 15 November 2010.
1 Warm-up Solve the following rational equation.
Definition: A rational function is a function that can be written where p(x) and q(x) are polynomials. 8) Graph Steps to graphing a rational function.
Graphing Rational Functions
HOMEWORK: WB p.31 (don’t graph!) & p.34 #1-4. RATIONAL FUNCTIONS: HORIZONTAL ASYMPTOTES & INTERCEPTS.
MAT 150 – Class #24 Topics: Graphing Rational Functions Asymptotes Vertical Slanted Horizontals Holes.
6) 7) 8) 9) 10) 11) Go Over Quiz Review Remember to graph and plot all points, holes, and asymptotes.
Advanced Algebra Dr. Shildneck Spring, Things to Remember:  Vertical Asymptotes come from the denominator  Horizontal Asymptotes result from smaller.
Graphing Rational Functions. I. Rational Functions Let P(x) and Q(x) be polynomial functions with no common factors and, then is a rational function.
Rational Functions Learning Objective: To find vertical asymptotes, horizontal asymptotes, holes, and one or two key points, then graph rational functions.
An x-intercept of a graph is the x- coordinate of a point where the graph crosses the x-axis. An y-intercept of a graph is the y- coordinate of a point.
Key Information Starting Last Unit Today –Graphing –Factoring –Solving Equations –Common Denominators –Domain and Range (Interval Notation) Factoring will.
WHO WANTS TO BE AN ALGEBRA 1 MILLIONAIRE?. $100 Plot the following Points: (0,0), (3,-2), (-4,6), (-1,-5), (2,3)
2.6 Rational Functions Steps for Graphing guidelines.
Graphing Rational Functions Objective: To graph rational functions without a calculator.
Graphing Rational Equations (Yeay for Graphing) TS: Demonstrating Understanding of Concepts Grab a whiteboard, a tissue for an eraser and marker on your.
Sketching the Graphs of Rational Equations 18 November 2010.
 Review:  Graph: #3 on Graphing Calc to see how it looks. › HA, VA, Zeros, Y-int.
Removable Discontinuities & Vertical Asymptotes
Chapter 8: Rationals 8.4 Multiplying and Dividing RationalsYellow Quiz: 5, 6 Page 605: Page 607: Page 1017: Graphing RationalsYellow.
1 Warm-up Solve the following rational equation.
Precalculus Section Objective: To sketch graphs of rational functions Refer to “Quick Guide to Rational Functions.”
Table of Contents Rational Functions: Sketching Graphs Example: Sketch the graph of, First find the intercepts. To find the x-intercept(s), set f (x) =
Graphing Rational Functions Example #8 PreviousPreviousSlide #1 NextNext We want to graph this rational function showing all relevant characteristics.
Warm-Up 1. Write the following in Slope-Intercept From: 2. Given the following table, write the exponential model: X01234 Y
Warm-Up 4 minutes Solve each equation. 1) x + 5 = 02) 5x = 03) 5x + 2 = 0 4) x 2 - 5x = 05) x 2 – 5x – 14 = 06) x 3 + 3x 2 – 54x = 0.
Sketching graph of a rational funtion Rational Functions Domain, Horizontal Assymptote, and Vertical Assymptote.
WHO WANTS TO BE AN ALGEBRA 1 MILLIONAIRE?. $100 Plot the following Points: (0,0), (3,-2), (-4,6), (-1,-5), (2,3)
Add Holes. Section 2.6 Rational Functions Grab out a calc!
CHAPTER 9 SECTION 3 RATIONAL FUNCTIONS AND GRAPHS Algebra 2 Notes May 21, 2009.
Table of Contents Graphing Quadratic Functions – General Form It is assumed that you have already viewed the previous three slide shows titled Graphing.
Notes Over 9.2 Graphing a Rational Function The graph of a has the following characteristics. Horizontal asymptotes: center: Then plot 2 points to the.
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:
Analyzing and sketching the graph of a rational function Rational Functions.
Twenty Questions Rational Functions Twenty Questions
Warm-Up: FACTOR 1.x 2 – x x x 2 – x – 2 5.x 2 – 5x – x 2 – 19x – 5 7.3x x - 8.
Rational Functions By: Elena Fayda, Ana Maroto, Madelynn Walker.
2.6 – Rational Functions. Domain & Range of Rational Functions Domain: x values of graph, ↔ – All real number EXCEPT Vertical Asymptote : (What makes.
Warm-up Complete the 5 question quiz for your warm-up today.
Rational Functions Algebra
Section 3.5 Rational Functions and Their Graphs
Section 5.4 Limits, Continuity, and Rational Functions
“Onions have layers.”.
Graphing Rational Functions
Notes Over 9.3 Graphing a Rational Function (m < n)
“Onions have layers.”.
Graphing Rational Expressions
27 – Graphing Rational Functions No Calculator
Section 5.4 Limits, Continuity, and Rational Functions
Presentation transcript:

HOMEWORK: WB p.28-30

RATIONAL FUNCTIONS: GRAPHING

BEST STEPS FOR GRAPHING: Step 1: Find and draw any horizontal asymptotes (dashed line). Step 2: Factor the equation if possible. Step 3: Find any holes. Then plot them. (plug the x-value into your reduced equation to find the y-value) Step 4: Find and draw any vertical asymptotes (dashed lines). Step 5: Plot the x- and y-intercepts Step 6: Graph the rest of the function (create a table, use your calculator).

WB P.34 #5 HA: Holes: VA: X-int: Y-int:

WB P.35 #13 HA: Holes: VA: X-int: Y-int:

WB P.34 #5 HA: Holes: VA: X-int: Y-int: