Advanced Algebra Dr. Shildneck Spring, 2015. Things to Remember:  Vertical Asymptotes come from the denominator  Horizontal Asymptotes result from smaller.

Slides:

Advertisements

Similar presentations

Holes & Slant Asymptotes

Advertisements

Rational Expressions GRAPHING.

2.7 Rational Functions and Their Graphs Graphing Rational Functions.

Discussion X-intercepts.

Warm-Up: FACTOR 1.x 2 – x x x 2 – x – 2 5.x 2 – 5x – x 2 – 19x – 5 7.3x x - 8.

4.4 Rational Functions Objectives:

Section 7.2.  A rational function, f is a quotient of polynomials. That is, where P(x) and Q(x) are polynomials and Q(x) ≠ 0.

ACT Class Openers:

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

2.7 Rational Functions By: Meteor, Al Caul, O.C., and The Pizz.

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

Today in Pre-Calculus Go over homework Notes: Homework

Solving for the Discontinuities of Rational Equations.

2.6 & 2.7 Rational Functions and Their Graphs 2.6 & 2.7 Rational Functions and Their Graphs Objectives: Identify and evaluate rational functions Graph.

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.

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

Class Work Find the real zeros by factoring. P(x) = x4 – 2x3 – 8x + 16

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.

Rational Functions and Their Graphs. Example Find the Domain of this Function. Solution: The domain of this function is the set of all real numbers not.

Chapter 3 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Rational Functions and Their Graphs.

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.

HOMEWORK: WB p.31 (don’t graph!) & p.34 #1-4. RATIONAL FUNCTIONS: HORIZONTAL ASYMPTOTES & INTERCEPTS.

Solving for the Discontinuities of Rational Equations.

6) 7) 8) 9) 10) 11) Go Over Quiz Review Remember to graph and plot all points, holes, and asymptotes.

Graphing Rational Functions Objective: To graph rational functions without a calculator.

 Review:  Graph: #3 on Graphing Calc to see how it looks. › HA, VA, Zeros, Y-int.

As x approaches a constant, c, the y coordinates approach – or +. As x approaches – or + the y coordinates approach a constant c. As x approaches – or.

Graphing Rational Functions Section 2-6 Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Objectives Identify Graph Discontinuities.

1 Warm-up Solve the following rational equation.

Bellwork 1.Identify any vertical and horizontal asymptotes, or holes in the graphs of the following functions. 2. Write a polynomial function with least.

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

Graphing Rational Functions Example #8 PreviousPreviousSlide #1 NextNext We want to graph this rational function showing all relevant characteristics.

Solving for the Discontinuities of Rational Equations 16 March 2011.

MATH 1330 Section 2.3. Rational Functions and Their Graphs.

GRAPHING RATIONAL FUNCTIONS. Warm Up 1) The volume V of gas varies inversely as the pressure P on it. If the volume is 240 under pressure of 30. Write.

Ch : Graphs of Rational Functions. Identifying Asymptotes Vertical Asymptotes –Set denominator equal to zero and solve: x = value Horizontal Asymptotes.

HOMEWORK: WB p RATIONAL FUNCTIONS: GRAPHING.

Analyzing and sketching the graph of a rational function Rational Functions.

Rational Functions. 6 values to consider 1)Domain 2)Horizontal Asymptotes 3)Vertical Asymptotes 4)Holes 5)Zeros 6)Slant Asymptotes.

Graphing Rational Functions Day 3. Graph with 2 Vertical Asymptotes Step 1Factor:

Twenty Questions Rational Functions Twenty Questions

Rational Functions & Solving NonLinear Inequalities Chapter 2 part 2.

Warm-Up: FACTOR 1.x 2 – x x x 2 – x – 2 5.x 2 – 5x – x 2 – 19x – 5 7.3x x - 8.

Chapter 2 – Polynomial and Rational Functions 2.6/7 – Graphs of Rational Functions and Asymptotes.

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.

Warm UpMar. 12 th  Solve each rational equation or inequality.

4.5 Rational Functions  For a rational function, find the domain and graph the function, identifying all of the asymptotes.

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.

GRAPHING SIMPLE RATIONAL FUNCTIONS. Investigation Graph the following using the normal window range. Draw a rough sketch of these functions on the back.

Find Holes and y – intercepts

Rational Functions…… and their Graphs

Horizontal Asymptotes

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

Graphing Rational Functions

Rational Functions (Algebraic Fractions)

Algebra 2/Trigonometry Name: ________________________

Ch. 2 – Limits and Continuity

Graphing Rational Functions

Graphing Polynomial Functions

Warm-Up: FACTOR x2 – 36 5x x + 7 x2 – x – 2 x2 – 5x – 14

Rational Function Discontinuities

Graphing Rational Functions

Graphing Rational Functions

2.6 Section 2.6.

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.

Presentation transcript:

Advanced Algebra Dr. Shildneck Spring, 2015

Things to Remember:  Vertical Asymptotes come from the denominator  Horizontal Asymptotes result from smaller or equal degrees in numerator  Slant Asymptotes result from dividing a 1-degree bigger numerator by the denominator

Things to Remember:  Y-Intercepts occur when x = 0.  X-Intercepts (zeros) occur when y = 0.  A General point occurs when x is plugged in to get a y-value.  Holes occur whenever there is a common factor between the numerator and denominator.

Things to Remember:  Whenever you are given a specific x-value, it’s related factor is (x – that number).  For example, given x = 5,  It’s factor is (x-5)  And given x = -5,  It’s factor is (x+5)

 Determine the vertical asymptotes (VA)  Write a factor for each in the denominator  Determine the horizontal asymptotes (HA)  Determine a factor that would result in that HA based on the rules for asymptotes  If there is a slant asymptote (SA), “un-divide” the numerator and denominator  In other words, multiply.  But! Then, add 1 to the answer.

 If there are holes, multiply in a factor in both the numerator and denominator.  If you are given a point (x, y):  make the constant part of the numerator a variable, like (x-b) or (x-h).  Plug in the x-value for x and set equal to the y-value  Solve for your variable constant

 Your final answer should be written as a function of x  It should start with “y =“ or “f(x)=“  It should have x variables and numbers. No other letters.  You may leave it in factored form.  Do not multiply out the factors.

Write an equation of a rational function with the following characteristics. VA: x = -7 HA: y = 0

Write an equation of a rational function with the following characteristics. VA: x = 12 HA: y = 3

Write an equation of a rational function with the following characteristics. VA: x = -3 HA: y = 1 Y-int: (0, 5)

Write an equation of a rational function with the following characteristics. VA: x = -1 HA: y = 2 Hole at: x = 5

Write an equation of a rational function with the following characteristics. VA: x = -1, x = 1 SA: y = 2x-3

Worksheet Number 7 Writing Equations of Rational Functions