Section 5.1 Determine if a function is a polynomial function. State the degree of a polynomial function.

Similar documents
Introduction. A rational function is a quotient of polynomial functions. It can be written in the form

Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14

Cumulative Review. Name. 13) 2x = -4 13) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Final Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i

The final is cumulative, but with more emphasis on chapters 3 and 4. There will be two parts.

Math 137 Exam #3 Review Guide

PreCalculus: Semester 1 Final Exam Review

11 /2 12 /2 13 /6 14 /14 15 /8 16 /8 17 /25 18 /2 19 /4 20 /8

Department of Mathematics, University of Wisconsin-Madison Math 114 Worksheet Sections (4.1),

Part I: Multiple Choice Questions

MATH 1314 College Algebra Scott Travis Fall 2014 Review for Exam #2

Mock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28}

MAT116 Final Review Session Chapter 3: Polynomial and Rational Functions

Algebra II CP Final Exam Review Packet. Calculator Questions

INTERNET MAT 117 Review Problems. (1) Let us consider the circle with equation. (b) Find the center and the radius of the circle given above.

Use a graphing utility to approximate the real solutions, if any, of the equation rounded to two decimal places. 4) x3-6x + 3 = 0 (-5,5) 4)

Exp, Log, Poly Functions Quarter 3 Review Name

More Polynomial Equations Section 6.4

Chapter 3: Polynomial and Rational Functions

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Review all the activities leading to Midterm 3. Review all the problems in the previous online homework sets (8+9+10).

A Partial List of Topics: Math Spring 2009

College Algebra and College Algebra with Review Final Review

Pre-Calculus Final Exam Review Units 1-3

Name. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

PreCalc Honors Summer Preparation

b) since the remainder is 0 I need to factor the numerator. Synthetic division tells me this is true

Math 120, Sample Final Fall 2015

1. Find the domain of the following functions. Write your answer using interval notation. (9 pts.)

GUIDED NOTES 5.6 RATIONAL FUNCTIONS

Algebra II Honors Final Exam Review

MAC1105-College Algebra

Polynomial Review Problems

H-Pre-Calculus Targets Chapter I can write quadratic functions in standard form and use the results to sketch graphs of the function.

Directions: Please read questions carefully. It is recommended that you do the Short Answer Section prior to doing the Multiple Choice.

NAME DATE PERIOD. Power and Radical Functions. New Vocabulary Fill in the blank with the correct term. positive integer.

Mathematics Precalculus: Academic Unit 1: Polynomial and Transcendental Functions

Polynomials. Exponents. End Behavior. Writing. Solving Factoring. Graphing. End Behavior. Polynomial Notes. Synthetic Division.

Teacher: Mr. Chafayay. Name: Class & Block : Date: ID: A. 3 Which function is represented by the graph?

Miller Objectives Alignment Math

SB CH 2 answers.notebook. November 05, Warm Up. Oct 8 10:36 AM. Oct 5 2:22 PM. Oct 8 9:22 AM. Oct 8 9:19 AM. Oct 8 9:26 AM.

Honors Algebra II Spring 2016 Final Exam Format

INDEX UNIT 3 TSFX REFERENCE MATERIALS 2014 ALGEBRA AND ARITHMETIC

Rational Exponents. Polynomial function of degree n: with leading coefficient,, with maximum number of turning points is given by (n-1)

INTERNET MAT 117. Solution for the Review Problems. (1) Let us consider the circle with equation. x 2 + 2x + y 2 + 3y = 3 4. (x + 1) 2 + (y + 3 2

Skill 6 Exponential and Logarithmic Functions

Algebra Review. Unit 7 Polynomials

Advanced Math Quiz Review Name: Dec Use Synthetic Division to divide the first polynomial by the second polynomial.

Princeton High School

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Algebra 2 Honors: Final Exam Review

Final Exam Review Part 2

MAT 107 College Algebra Fall 2013 Name. Final Exam, Version X

COURSE SYLLABUS Part I Course Title: MATH College Algebra Credit Hours: 4, (4 Lecture 0 Lab G) OTM-TMM001

Review Guideline for Final

Rational Functions 4.5

of multiplicity two. The sign of the polynomial is shown in the table below

f(x) = 2x + 5 3x 1. f 1 (x) = x + 5 3x 2. f(x) = 102x x

Calculus First Semester Review Name: Section: Evaluate the function: (g o f )( 2) f (x + h) f (x) h. m(x + h) m(x)

Horizontal and Vertical Asymptotes from section 2.6

Topics from Algebra and Pre-Calculus. (Key contains solved problems)

Learning Target: I can sketch the graphs of rational functions without a calculator. a. Determine the equation(s) of the asymptotes.

Rational Functions. Elementary Functions. Algebra with mixed fractions. Algebra with mixed fractions

3. Solve the following inequalities and express your answer in interval notation.

M30-1: Polynomial, Radical and Rational Functions, Graphs and Equations Exam /20

Chapter 2 Polynomial and Rational Functions

Polynomial Functions and Models

Catholic Central High School

1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.

EXAM 3 Tuesday, March 18, 2003

Chapter. Part 1: Consider the function

Final Exam Review Problems

Skills Practice Skills Practice for Lesson 10.1

Solutions to MAT 117 Test #3

Section Properties of Rational Expressions

Algebra II Double Period Final Exam Review. 3. Solve. 4. Solve.


Midterm Review. Name: Class: Date: ID: A. Short Answer. 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

ID: ID: ID: of 39 1/18/ :43 AM. Student: Date: Instructor: Alfredo Alvarez Course: 2017 Spring Math 1314

Chapter 2: Polynomial and Rational Functions

To get horizontal and slant asymptotes algebraically we need to know about end behaviour for rational functions.

NONLINEAR FUNCTIONS A. Absolute Value Exercises: 2. We need to scale the graph of Qx ( )

College Algebra Final Exam

Pre-Calculus Chapter 0. Solving Equations and Inequalities 0.1 Solving Equations with Absolute Value 0.2 Solving Quadratic Equations

Practice Test - Chapter 2

Lesson 2.1: Quadratic Functions

Math 108 Final Exam Page 1 NO CALCULATORS OR CELL PHONES ALLOWED.

Pre-calculus 12 Curriculum Outcomes Framework (110 hours)

GOOD LUCK! 2. a b c d e 12. a b c d e. 3. a b c d e 13. a b c d e. 4. a b c d e 14. a b c d e. 5. a b c d e 15. a b c d e. 6. a b c d e 16.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. B) 6x + 4

Math 2412 Activity 2(Due by EOC Feb. 27) Find the quadratic function that satisfies the given conditions. Show your work!

4.3 Division of Polynomials

Section 4.5 Graphs of Logarithmic Functions

Skill 6 Exponential and Logarithmic Functions

INSTRUCTIONS USEFUL FORMULAS

HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK

UNIT 3 MATHEMATICAL METHODS ALGEBRA

Exponential and Logarithmic Functions. Copyright Cengage Learning. All rights reserved.

ARE YOU READY 4 CALCULUS

Transcription:

Test Instructions

Objectives Section 5.1 Section 5.1 Determine if a function is a polynomial function. State the degree of a polynomial function. Form a polynomial whose zeros and degree are given. Graph transformations (vertical shifts, horizontal shifts, and reflections) of power functions. Find the zeros and multiplicities of a polynomial function and use them to Find the zeros and multiplicities of a polynomial function and use them to determine whether the graph crosses or touches at each x-intercept. Remember that zeros are the x-coordinates of the x-intercepts. Find the y- intercept. Be able to state the power function that f resembles for large values of x and state the maximum number of turning points. Determine the behavior of the graph near the x-intercepts. Graph the function.

Review Problem Section 5.1 Fall 2006 Final Exam Determine the maximum number of turning points on the graph of f(x). Determine the behavior of the graph of fnear each x- intercept.

Objectives Section 5.2 Section 5.2 Find the domain of a rational function. Find vertical and horizontal or oblique asymptotes

Review Problem Section 5.2 Fall 2007 Final Exam

Finding Asymptotes pg 351

Review Problem Section 5.2 Fall 2007 Final Exam

Objectives Section 5.3 Section 5.3 Graph a rational function by analyzing the function: Find the domain, any asymptotes, any intercepts, and sketch the graph. Given the graph of a rational function, find the domain and range, any intercepts, and any asymptotes. Use your graphing calculator to find the approximate maximum value of a function in an applied (word) problem.

Review Problem Section 5.3 Fall 2006 Final Exam

Section 5.4 Solve rational and polynomial inequalities. Objectives Section 5.4

Review Problem Section 5.4 Fall 2007 Final Exam

Review Problem Section 5.4 Fall 2009 Final Exam

Objectives Section R.6 Section R.6 Use synthetic division to find the quotient and remainder. Use synthetic division to determine whether x-c is a factor of f(x).

Review Problem Section R.6/Ch 6 Fall 2008 Final Exam

Objectives Section 5.5 Section 5.5 Use the Factor Theorem to determine whether x-c is a factor of f(x). Know the maximum number of zeros a polynomial may have. List the potential rational zeros of a polynomial function. (Use the Rational Zeros Theorem.) Use the above information to find the real zeros of a polynomial function and write the function in factored form. Solve polynomial equations in the real number system by using the above information.

Review Problem Section 5.5 Fall 2006 Final Exam

Objectives Section 5.6 Section 5.6 Given the degree and some zeros of a polynomial with real coefficients, find the remaining complex zeros. Form a polynomial f(x) having given degree and complex zeros. Find the complex zeros of a polynomial function and write the function in factored form.

Review Problem Section 5.6 Fall 2006 Final Exam

Review Problem Section 5.6 Fall 2008 Final Exam

Objectives Section 6.1 Section 6.1 Find the composite of two functions at a given value of x. Find the composite of two functions and the domain of the composite function.

Review Problem Section 6.1 Fall 2007 Final Exam

Objectives Section 6.2 Section 6.2 Determine whether a function is one-to-one. Determine if two functions f and g are inverses of each other. Find the inverse of a function and state the domain and range of both and f 1 ( x). f ( x)

Review Problem Section 6.2 Fall 2007 Final Exam

Review Problem Section 6.2 Fall 2008 Final Exam

Objectives Section 6.3 Section 6.3 Graph without using a calculator in this section! x x Graph an exponential function f ( x) = a and transformations of f ( x) = a. State the domain, range, and horizontal asymptote. u v Solve exponential equations by using: If a = a then u = v.

Review Problem Section 6.3 Fall 2007 Final Exam

Review Problem Section 6.3 Fall 2005 Final Exam

Objectives Section 6.4 Section 6.4 Graph without using a calculator in this section! Change between exponential and logarithmic form of an equation. Find the exact value of a logarithm. Find the domain of a logarithmic function. Graph y = log a x, y = ln( x), and transformations of each. State the domain, range, and vertical asymptote. Solve logarithmic equations by changing to exponential form.

Review Problem Section 6.4 Fall 2007 Final Exam

Objectives Section 6.5 Section 6.5 Write an expression as a sum and/or difference of logarithms. Express powers as factors. Write an expression as a single logarithm.

Review Problem Section 6.5 Fall 2006 Final Exam

Section 6.6 Solve logarithmic and exponential equations. Be able to give the exact solution. Remember to check that solutions to logarithmic equations are in the domain. Objectives Section 6.6

Review Problem Section 6.6 Fall 2007 Final Exam

Section 6.7 Solve application problems involving compound interest. You will need a calculator. Objectives Section 6.7

Review Problem Section 6.7 Fall 2007 Final Exam

Review Problem Section 6.7 Fall 2008 Final Exam

Section 6.8 Solve application problems involving exponential growth and decay. Know how to find or use half-life of a substance in solving problems. You will need a calculator. Objectives Section 6.8

Review Problem Section 6.8 Final Exam Fall 2007

Review Problem Section 6.8 Final Exam Fall 2006