Deadline: Sunday, March 29, 2009
Remember to check announcements and messages in MyMathLab daily.
a. Objectives
This lesson covers sections 8.1, 5.1 and 5.5 in your textbook and Quiz 7. When you complete this lesson you should be able to solve each of the following types of problems, showing all relevant steps:
8.1.1. Solve systems of equations by substitution.
8.1.2. Solve systems of equations by elimination.
8.1.3. Identify inconsistent systems of equations (two variables).
8.1.4. Express the solution of a system of dependent equations (two variables).
8.1.5. Solve systems of three equations containing three variables.
8.1.6. Identify inconsistent systems of equations (three variables).
8.1.7. Express the solution of a system of dependent equations (three variables).
5.1.1. Identify polynomial functions, and find the degree of a polynomial function.
5.1.2. Graph power functions of the form f(x)=x^n where n is an even integer. Label three points on the graph, and sketch the proper shape.
5.1.3. Graph power functions of the form f(x)=x^n where n is an odd integer. Label three points on the graph, and sketch the proper shape.
5.1.4. Find a polynomial that has a given degree and given zeros.
5.1.5. Identify the real zeros of a polynomial function and find their multiplicity. Use the multiplicity of a given zero to determine if the graph crosses or touches the x-axis at that zero.
5.1.6. Use a chart to determine whether the graph is above or below the x-axis on each side of a given zero.
5.1.7. Determine the maximum number of turning points on the graph of a given polynomial function.
5.1.8. Determine the end behavior of a polynomial function from its degree.
5.1.9. Distinguish between graphs of polynominal functions and other functions by knowing that polynomial functions have graphs that are smooth with no breaks, gaps, or sharp points.
5.1.10. Graph polynomial functions using the six-step method shown in the textbook. Show work for each step. On the graph, label all intercepts.
5.5.1. Use the remainder and factor theorems.
5.5.2. Use the Rational Zeros Theorem to list the potential rational zeros of a polynomial function.
5.5.3. Find the real zeros of a polynomial function by using the Rational Zeros Theorem, synthetic division and the "depressed equation" concept.
5.5.4. Solve polynomial equations by using the Rational Zeros Theorem, synthetic division and the "depressed equation" concept.
b. Assignments and Due Dates
All assignments for Lesson 7 must be completed and submitted by 11:59pm on Sunday, March 29, 2009. Assignments for this lesson include:
1. Learn the material in 8.1 by using "E-text, Videos, Practice" (study the text, view videos, do example problems and practice problems) AND/OR using the "Lecture Notes" (read the lecture notes, work out the examples, and check your answers using the key). Both are accessed through the MyMathLab (MML) menu on the left of this page.
2. Complete the homework assignment for 8.1. Homework assignments are accessed through "Homework" on MML menu on the left.
3. Learn the material in 5.1 by using "E-text, Videos, Practice" (study the text, view videos, do example problems and practice problems) AND/OR using the "Lecture Notes" (read the lecture notes, work out the examples, and check your answers using the key). Both are accessed through the MyMathLab (MML) menu on the left of this page.
4. Complete the homework assignment for 5.1. Homework assignments are accessed through "Homework" on MML menu on the left.
5. Learn the material in 5.5 by using"E-text, Videos, Practice" (study the text, view videos, do example problems and practice problems) AND/OR using the "Lecture Notes" (read the lecture notes, work out the examples, and check your answers using the key). Both are accessed through the MML menu on the left of this page.
6. Complete the homework assignment for 5.5. Homework assignments are accessed through "Homework" on the MML menu on the left.
7. Complete and submit Quiz 7. Quizzes are accessed through "Quizzes/Test Rev" on the MML menu on the left.
Online College Algebra Lessons
Created by Carol Congleton, ccongleton@miracosta.edu
Mathematics Department
MiraCosta College
Graphics files used with permission of Richard S. Palais
http://rsp.math.brandeis.edu/3D-XplorMath/Surface/gallery.html
Lesson 7: Sections 8.1, 5.1 and 5.5; Quiz 7
