Reading Assignments for PreCalculus
Fall 1997, Math 100
Chapter 4
Be sure to check back often, because assignments may change!
Last modified: November 3,1997
10/24, respond by 8am 10/27
Section 4.1 Polynomial Functions
 To read: page 179middle of page 186
 Be sure to understand:The definition of a polynomial; the distinction and relationship between the zeros of a function and the roots of an equation.
 Reading questions:
 Consider the function y=6x^2+7x3.
(a) What is the effect of the highest power being 2?
(b) What is the effect of the leading coefficient being 6?
(c) What is the effect of the constant being 3?
 A quadratic function (a parabola) always has 2 zeros. What are the three ways these could occur, and what graphical significance do they have?
 Email subject line: Math 100 Your Name 10/24
10/27, respond by 8am 10/29
Section 4.1 Polynomial Functions
Respond to yesterday's questions, if you didn't already.
10/29, respond by 8am 10/31
Section 4.1 Polynomial Functions
Section 4.3 The Roots of Polynomial Equations: Real or
Complex?
 To read: page 186page 189; page 199page 206
 Be sure to understand:page 199
 Reading questions:
 Examine the graph of f(x)=(x+1)(x2)(x4)^3 using a grapher.
(a) What is the degree of this polynomial? (Do NOT multiply it all out!)
(b) What happens near the triple root x=4?
(c) What is the end behavior of this polynomial?
 Give a graphical explanation for why a cubic must have at least one real root whie a quadratic can have none.

 Email subject line: Math 100 Your Name 10/29
10/31, respond by 8am 11/03
Section 4.4 Building New Functions From Old
 To read: Page 208 the middle of page 213
 Be sure to understand:the bottom of page 208, the bottom of page 209, Example 2
 Reading questions:
Consider R(x)=(2x^2+1)/(x^21)=(2x^2+1)/[(x1)(x+1)].
 Calculate R(1.0001), R(.9999), R(.9999), R(1.0001).
 What can you conclude happens to the graph of R(x) near 1 and 1?
 Calculate R(1000), R(100,000), R(1000), R(100,000).
 What can you conclude about the end behavior of the graph of R(x)?
 Email subject line: Math 100 Your Name 10/31
11/03, respond by 8am 11/05
Section 4.4 Building New Functions From Old
 To read: Reread pages 208213, and read 213219
 Reading questions:
 How does 5^x behave when x is very large? How does x^(1) behave when x is very large? Which behavior dominates in the product x^(1) 5^x? In other words, which function controls the behavior for large x, in the product?
 Consider R(x)=(x^24)/2(x^21).
 Where does R(x) have zeros?
 Where does R(x) have vertical asymptotes?
 What is the end behavior of R(x)?
 What does it mean to take the composition of two functions?
 Email subject line: Math 100 Your Name 11/3
11/05, respond by 8am 11/07
Section 4.4 Building New Functions From Old
 To read: Page 213Page 219
 Reading questions:
 If f(x)=x^2 and g(x)=2x, find f(g(x)) and g(f(x)). Are they the same or different?
 Does h(h^(1)(x))=h^(1)(h(x))? (What do they each equal?)
 How do j(x)+4, j(x), and j(x+4) differ graphically (for any function j(x))?
 Email subject line: Math 100 Your Name 11/5
11/07, respond by 8am 11/10
Section 4.6 Finding Polynomial Patterns
 To read: Page 232the bottom of page 237
 Be sure to understand:how you tell if a set of points lies on a quadratic or a cubic; Example 1.
 Reading questions:
 Show that the points (3,35), (2,21), (1,11), (0,5), (1,3), (2,5) all lie on a parabola.
 Describe how you would go about finding the equation of the parabola in (1).
 Also be sure to:study for the 2nd gateway exam!
 Email subject line: Math 100 Your Name 11/7
11/10, respond by 8am 11/12
Section 4.6 Finding Polynomial Patterns
 To read: bottom of page 237page 245
 Be sure to understand:Middle of page 242; Example 4.
 Reading questions:
 How many (noncolinear) points are needed to uniquely determine an 8th degree polynomial?
 When is finding an interpolating polynomial a good idea? When is it a bad idea?
 Email subject line: Math 100 Your Name 11/10
11/12, for 11/14
Project 2
 To read: Project 2, Guide to Writing a Math Paper, and the comments made on your last project
 Be sure to understand:All of it
 Also be sure to:
start thinking about an approach, and to make contact with a partner. I suggest you work with somebody different this time, although as always, several groups may work together.
Here Endeth Chapter 4
Now we move on to Chapter 7
Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 027660930
TEL (508) 2863973
FAX (508) 2858278
jsklensk@wheatonma.edu
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