Reading Assignments for Precalculus
Fall 1998, Math 100
CHAPTER 4
Be sure to check back often, because assignments may change!
Last modified: November 12, 1998
Due 10/28 at 8am, assigned 10/26
Section 4.1: Polynomial Functions
- To read: Section 4.1: page 179 - middle of page 184
- Be sure to understand: How the behavior of polynomials can differ from the other families of functions we've studied. What the degree of a polynomial is. The connections between power functions, linear functions, and polynomials. The difference between a function and an equation; the difference between zeros and roots. The connection between real roots, x-intercepts, and linear factors. Know how to use the quadratic formula, of course.
- Reading questions:
- For each family of functions we've discussed so far, how many turning points can such a function have? How many inflection points? What can polynomials do that the others can not?
- Construct a quadratic polynomial with real roots of x=2 and x=4.
- Briefly describe the graph of f(x)=-3x^{2}+4.
- Reminder: Next midterm is 11/5.
- E-mail Subject Line: Math 100 Your Name 10/28
Due 10/30 at 8am, assigned 10/28
Section 4.1: Polynomial Functions
- To read: Finish Section 4.1
- Be sure to understand: How many roots a cubic polynomial can have; how many real roots a cubic polynomial can have; the connection between real roots, x-intercepts, and linear factors.
- Reading questions:
- How many turning points does a quadratic polynomial have? How about inflection points?
- How many turning points does a cubic polynomial have? How about inflection points?
- Construct a cubic polynomial with roots x=-1, x=2, and x=4.
- Can a cubic polynomial have 2 real roots and 1 imaginary root?
- Reminder: Next midterm is 11/5. It will cover through Section 4.1.
- E-mail Subject Line: Math 100 Your Name 10/30
Due 11/2 at 8am, assigned 10/30
Section 4.1: Polynomial Functions
Section 4.3: The Roots of Polynomial Equations
- To read: Re-read Section 4.1: middle of p. 186-189; Section 4.3: pages 199-206
- Be sure to understand: How many roots an nth degree polynomial has; how many real roots an nth degree polynomial can have; what teh real roots mean on a graph; how to find a polynomial, knowing its degree, roots, and y-intercept; the connection between a repeated root and the behavior of the graph at that point.
- Reading questions:
- Find a 4th degree polynomial with roots x=2, x=1, x=-1, x=0, and vertical intercept y=3.
- If a polynomial has a double root at x=2, does the polynomial function corss teh x-axis at x=2? Have a turning point at x=2? Have an inflection point at x=2? Some combnination of the above?
- Use your function grapher to graph a function with a triple root, for instance
f(x)=(x-2)^3(x-4). How does the function behave at the triple root of x=2?
- Reminder: Next midterm is 11/5. It will cover through Section 4.1. Sign up for an exam time! (You can do it by e-mail. If you pick a time I won't be here, I'll just reply by e-mail.)
- E-mail Subject Line: Math 100 Your Name 11/2
Due 11/4 at 8am, assigned 11/2
Section 4.4: Building New Functions From Old
- To read: Section 4.4: p. 208-middle of p. 213
- Be sure to understand: how you get the graph of (f+g)(x) from the graphs of f(x) and g(x); how to analyze the behavior of (fg)(x) and (f/g)(x)--which terms dominate, any asymptotes, etc.
- Reading questions:
- If f(x)=3x-4 and g(x)=1/x, find
- (f+g)(3)
- (f-g)(3)
- (fg)(3)
- (f/g)(3)
- Consider
R(x)=(3x^{3}+5)/(x^{3}-x^{2}+x-1)
- Calculate R(.99), R(.999), R(1.01), R(1.001).
- What would you guess happens to the graph of R(x) near x=1, based on
your answers to the previous question.
- Calculate R(100), R(1000), R(100,000).
- What would you guess happens to the graph of R(x) as x approaches infinity?
- Keep on studying!: If you haven't already signed up for an exam time, e-mail me!
- E-mail Subject Line: Math 100 Your Name 11/4
Due 11/6 at 8am, assigned 11/4
Take a break, since we're behind anyway!
Due 11/9 at 8am, assigned 11/6
Section 4.4: Building New Functions From Old
- To read: Section 4.4: p. 213-middle of p. 219
- Be sure to understand: what a composition of functions is; vertical and horizontal shifts, stretching and compressing by multiplying by a constant.
- Reading questions:
Let f(x)=x^{3}+3x^{2} and g(x)=10^{x}.
- Find f o g(x)
- Find g o f(x)
- Create a new function h(x) whose graph is identical to that of f(x), but shifted up by 4 units.
- Create a new function j(x) whose graph is identical to that of g(x), but shifted right 4 units.
- E-mail Subject Line: Math 100 Your Name 11/9
Due 11/11 at 8am, assigned 11/9
Section 4.6: Finding Polynomial Patterns
- To read: Section 4.6: pp 232-234;
skim 235-middle of p. 241
read middle of p. 241-p. 245
- Be sure to understand:2nd and 3rd differences. If you have 6 distinct points (with different independent variables), what is the smallest degree polynomial that is guaranteed to contain them? Example 4.
- Reading questions:
- Construct an interpolating polynomial of degree 2 that goes through the points P(0,6), Q(1,0), and R(2,-2).
- E-mail Subject Line: Math 100 Your Name 11/11
Due 11/13 at 8am, assigned 11/11
Section 4.4 and Section 4.6
- To read: re-read all of sections 4.4 and 4.6.
- Be sure to understand: composition, shifts, interpolating polynomials
- Reading questions:
None, just really work on understanding it.
Due 11/16 at 8am, assigned 11/13
Project 2!
- To read: the project, the writing guidelines, and the comments I made on your last paper
- Be sure to understand: what the project is asking. I suggest you start thinking about it over the week-end, so that you can use your class time most efficiently.
- Reading questions:
None, just get started on solving this puzzling problem.
And on to trigonometry we go! Next stop, Chapter 7!
Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278
jsklensk@wheatonma.edu
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