Final Exam Part 1 (optional but recommended)

Slides:



Advertisements
Similar presentations
Functions AII.7 e Objectives: Find the Vertical Asymptotes Find the Horizontal Asymptotes.
Advertisements

Rational Expressions GRAPHING.
Power Functions and Models; Polynomial Functions and Models February 8, 2007.
(a) (b) (c) (d). What is (1,2,3)  (3,4,2)? (a) (1, 2, 3, 4) (b) (1,2)  (3,4) (c) (1,3,4,2) (d) (3,1)  (4,2)
Other types of Equations Polynomial Equations. Factoring Solve.
RATIONAL FUNCTIONS 2.6. RATIONAL FUNCTIONS VERTICAL ASYMPTOTES  To find vertical asymptotes first reduce the function if possible.  Set the denominator.
Polynomial and Rational Functions
Chapter 6. By the end of this section, you will be able to: 1. Evaluate polynomial functions; 2. Identify general shapes of graphs od polynomial functions.
ACT Class Openers:
Polynomial Functions and Models Section 5.1. Polynomial Functions.
Notes Over 3.2 Graphs of Polynomial Functions Continuous Functions Non-Continuous Functions Polynomial functions are continuous.
Limits at Infinity Explore the End Behavior of a function.
7.1 and 7.2 Graphing Inequalities 7.3 Solving Equations Using Quadratic Techniques Algebra II w/ trig.
Section 2.6 Rational Functions Part 1
6.5 The Remainder and Factor Theorems p. 352 How do you divide polynomials? What is the remainder theorem? What is the difference between synthetic substitution.
Lesson 2.6 Rational Functions and Asymptotes. Graph the function: Domain: Range: Increasing/Decreasing: Line that creates a split in the graph:
Math 160 Notes Packet #7 Polynomial Functions 1. 2.
Graphing Polynomials. Step One: Determine End Behavior Using Lead Coefficient Test.
Graphs of Polynomial Functions. Parent Graphs  Quadratic Cubic Important points: (0,0)(-1,-1),(0,0),(1,1)  QuarticQuintic  (0,0) (-1,-1),(0,0),(1,1)
7.4 The Remainder and Factor Theorems Use Synthetic Substitution to find Remainders.
Do Now: Solve the inequality. Academy Algebra II/Trig 5.1: Polynomial Functions and Models HW: p.340 (12, 13, 17-20, 40, 41, 43, – parts a,d,e only)
UNIT 2, LESSON 1 POLYNOMIAL FUNCTIONS. WHAT IS A POLYNOMIAL FUNCTION? Coefficients must be real numbers. Exponents must be whole numbers.
Graphs of polynomials a n > 0a n < 0 n even n odd f(x)=x 3 +2x 2 -x-2g(x)=-x 4 +5x 2 -4 degree 3degree 4 degree n h(x)=a n x n +a n-1 x n-1 +…+a 1 x+a.
Polynomial P(x) Binomial Factors Polynomial P(x) Binomial Factors Solutions of P(x)=0 Zeros of P(x)
Solving equations with polynomials – part 2. n² -7n -30 = 0 ( )( )n n 1 · 30 2 · 15 3 · 10 5 · n + 3 = 0 n – 10 = n = -3n = 10 =
5-2 Polynomials, Linear Factors, & Zeros
Polynomials of Higher Degree 2-2. Polynomials and Their Graphs  Polynomials will always be continuous  Polynomials will always have smooth turns.
1 Limits at Infinity Section Horizontal Asymptotes The line y = L is a horizontal asymptote of the graph of f if.
15.10 Graphing Polynomial Functions OBJ:  To sketch the graph of an integral polynomial function of degree n with n distinct roots.
Using Multiplicity and Graphs to Determine Equations 8 November 2010.
2.5 The Fundamental Theorem of Algebra. The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra – If f(x) is a polynomial of degree n, where.
Source Page US:official&tbm=isch&tbnid=Mli6kxZ3HfiCRM:&imgrefurl=
Every polynomial P(x) of degree n>0 has at least one zero in the complex number system. N Zeros Theorem Every polynomial P(x) of degree n>0 can be expressed.
Conjugate Pairs Theorem Every complex polynomial function of degree n  1 has exactly n complex zeros, some of which may repeat. 1) A polynomial function.
Section 4.1 Polynomial Functions and Models.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 5.1 Polynomial Functions and Models.
THE GRAPH OF A POLYNOMIAL FUNCTION. Review: The Degree of a Polynomial  The degree of a polynomial is equal to the power of its highest power of x. 
 Polynomial Functions of Higher Degree.  Use transformations to sketch graphs of polynomial functions.  Use the Leading Coefficient Test to determine.
Algebra Rational Functions. Introduction  Rational Function – can be written in the form f(x) = N(x)/D(x)  N(x) and D(x) are polynomials with.
Путешествуй со мной и узнаешь, где я сегодня побывал.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 5.1 Polynomial Functions and Models.
5-2 Polynomials, Linear Factors, & Zeros
Objective: To determine the end behavior of polynomial functions
Section 2.6 Rational Functions Part 2
Notes Over 3.4 The Rational Zero Test
7.4 The Remainder and Factor Theorems
Page 1. Page 2 Page 3 Page 4 Page 5 Page 6 Page 7.
Polynomial and Rational Functions
Bell ringer Simplify the following expressions as much as you can!
1. Use the quadratic formula to find all real zeros of the second-degree polynomial
Zeros of a Polynomial Function
Warm-up: Sketch the graph of f(x) = x5 – 4x4 + 4x3. Be sure to include all critical values. HW: Quiz Review 2.1/2.2.
Main Ideas Key Terms Chapter 2 Section 3 Graphing a Polynomial
Polynomial Functions and Their Graphs
Rational Functions  .
3.3 Polynomial Functions and Models
7.2 Polynomial Functions and Their Graphs
7.2 Graphing Polynomial Functions
2.6 Section 2.6.
Rational Functions Lesson 9.4.
Jeopardy Q $100 Q $100 Q $100 Q $100 Q $100 Q $200 Q $200 Q $200
3.3 Polynomial Functions and Models
19A-19E Cubic, Quartic, and Rational Functions
Homework Check.
Homework Check.
Students, Take out your calendar and your homework
Polynomial Functions and Models
Section 2.3: End Behavior of Polynomial Functions
End Behavior, Extrema & Sketching
 .
Presentation transcript:

Final Exam Part 1 (optional but recommended) Page 358, #41-43 only if you want extra help on these Page 371, #9, 11 Page 379, Study turning points and degree of polynomials and number of zeros Page 428, #3, 17-18, 25-26 ok to just find asymptotes Page 477, #87-91 odd Page 507, #53 Page 576, #5, 27 Page 622, #8 Page 50, #37, 39 Page 62, #33 Page 90, #89, a an c Page 153, #11, 13 Page 162, #35, 39 Page 179, #27, 39, 45 Page 273, #7-11 all Page 287, #75, 77, 81 Page 314, #55, 69, 71, 73 Page 338, #15,27,31,41 Page 347, #11, 15, 21