Find all the zeros of the functions.

Slides:



Advertisements
Similar presentations
3.4 Rational Functions I. A rational function is a function of the form Where p and q are polynomial functions and q is not the zero polynomial. The domain.
Advertisements

Section 5.3 – The Graph of a Rational Function
Graphs of Exponential and Logarithmic Functions
Warm-Up: FACTOR 1.x 2 – x x x 2 – x – 2 5.x 2 – 5x – x 2 – 19x – 5 7.3x x - 8.
Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.
EXAMPLE 1 Graph a rational function (m < n) Graph y =. State the domain and range. 6 x SOLUTION The degree of the numerator, 0, is less than the.
Section4.2 Rational Functions and Their Graphs. Rational Functions.
Objective: Graph rational functions. Identify slant asymptotes. Example 1 Analyze the function of a.Domain b.Range c.Symmetry d.End behavior.
Rational Functions & Their Graphs
 No quiz on dividing polynomials. Next assessment is Unit 2 test!  Continue to study by reviewing the vocabulary flash cards you’ve already made, doing.
Section 9-5 Hyperbolas. Objectives I can write equations for hyperbolas I can graph hyperbolas I can Complete the Square to obtain Standard Format of.
Introducing Oblique Asymptotes Horizontal Asymptote Rules: – If numerator and denominator have equal highest power, simplified fraction is the H.A. – If.
1 Warm-up Solve the following rational equation.
Rational Functions and Their Graphs
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 Intro - Chapter 4.4.  Let x = ___ to find y – intercepts A rational function is the _______ of two polynomials RATIO Graphs of Rational.
What is the symmetry? f(x)= x 3 –x.
Solve an equation using addition EXAMPLE 2 Solve x – 12 = 3. Horizontal format Vertical format x– 12 = 3 Write original equation. x – 12 = 3 Add 12 to.
Removable Discontinuities & Vertical Asymptotes
2.7Graphs of Rational Functions Students will analyze and sketch graphs of rational functions. Students will sketch graphs of rational functions that have.
Essential Question: How do you find intercepts, vertical asymptotes, horizontal asymptotes and holes? Students will write a summary describing the different.
Graphing Rational Functions Day 3. Graph with 2 Vertical Asymptotes Step 1Factor:
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 Graphing Review. #1 Find all vertical asymptotes and holes in the graph.
Find Holes and y – intercepts
Rational Functions A rational function has the form
Rational Functions and Asymptotes
Graphing Rational Functions Day 2
Section 2.6 Rational Functions Part 2
Polynomial and Rational Functions
Rational Functions.
Graphs of Rational Functions
28 – The Slant Asymptote No Calculator
Section 5.3 – The Graph of a Rational Function
1) Find the measure of the largest angle.
Lesson 2.7 Graphs of Rational Functions
Rational Functions and Their Graphs
Section 3.5 Rational Functions and Their Graphs
Section 5.4 Limits, Continuity, and Rational Functions
Graphing Rational Functions
Warm-Up: FACTOR x2 – 36 5x x + 7 x2 – x – 2 x2 – 5x – 14
Rational Function Discontinuities
Rational Functions and Asymptotes
Find all the solutions without using a calculator.
Notes Over 9.3 Graphing a Rational Function (m < n)
Factor completely and simplify. State the domain.
Bell Ringer Check your vocabulary….
Write each using Interval Notation. Write the domain of each function.
Students, Take out your calendar and your homework
Basics of Functions and Their Graphs
Chapter 4: Rational, Power, and Root Functions
Chapter 4: Rational, Power, and Root Functions
Rational Functions Section 8.3.
Students, Take out your calendar and your homework
Divide. Use synthetic division.
Students, Take out your calendar and your homework
Solve the following equations.
1) Write the vector in component form.
Find all the solutions without using a calculator.
(1) Find all of the zeros of f.
Students, Take out your calendar and your homework
Find all the real zeros of the functions.
Divide using long division.
Evaluate each expression. Hint: Use the unit circle.
Students, Take out your calendar and your homework
Multiply each expression.
Students, Take out your calendar and your homework
Section 5.4 Limits, Continuity, and Rational Functions
The Coordinate Plane #39.
Properties of Rational Functions The Graph of a Rational Function
Presentation transcript:

Find all the zeros of the functions. Students, Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary. Find all the zeros of the functions. Hint : List the possible zeros and test them. 2) Simplify.

JIGSAW Go into pairs, then group into 4’s number off from 1 to 4. Depending on your number, you will do the following problems on the next slide: Student #1: #4, 6 Student #2: #8, 10 Student #3: #14, 16 Student #4: #24, 26 Write down the problem numbers you will do now.

Next Formation of “expert” groups 2 groups of each number (1’s, 2’s, 3’s and 4’s) Work out only your problems in your expert groups (10 minutes.) Make sure your entire group agrees on the solutions.

Next Return to your original groups Complete all exercises on the slide. If you get stuck on a problem, ask your group’s expert.

Graph the following functions.

Find the domain, vertical asymptotes, horizontal asymptotes, zeros, and y-intercept of the functions. Are there any slant asymptotes?

Divide. Use synthetic division.

Perform the indicated operations.

Find the domain of the following functions.