Fall 1999, Math 100

CHAPTER 1

Be sure to check back often, because assignments may change!

Due Friday 9/10 at 9am

• Pay attention to: all of it: I tried to address as many issues as I could think of. Any questions? Ask me!
• Reminder: Keep this in your folder.

• Pay attention to: exam dates, especially first gateway. Project due dates. Date of final.
• Reminder: enter these dates in your calendar now.

Right Triangle Trigonometry handout

• Be sure to understand: definitions of 6 trig functions

Section 1.1 Functions All Around Us

• To read: p. 1-near the bottom of p. 4
• Be sure to understand: The definition of a function, all associated examples, how a graph can represent and even define a function.

E-mail Subject Line: Math 100 Your Name 9/10

1. Consider a right triangle with legs of length 6 and 8, and with hypotenuse of length 10. Let a be the angle formed by the hypotenuse and the leg of length 6. What cos(a) ?
2. Kenny weighs around 24 kg. Use Fig 1.1 to predict his metabolic rate.
3. Would you use Fig 1.1 to predict the metabolic rate for extinct mammoths? Why or why not?
4. What are the different ways functions can be given?
5. Consider the relationship between the time of day and the temperature in the dimple on Sept. 7.
• Given enough information, if I ask you the temperature at a certain time of day, could you always give me a precise answer with no ambiguity?
• Use your answer to determine whether the temperature depends on the time of day.
• Conclude whether or not temperature is a function of time of day.

• Given enough information, if I ask you what time a certain temperature was reached, could you always give me a precise answer with no ambiguity?
• Thus, determine whether time of day depends on the temperature.
• Conclude whether or not the time of day is a function of temperature.

Reminders:

• Remember to come to my office to take the gateway Thursday 9/9. It should really help the class flow smoothly for you, and I look forward to meeting each of you individually!
• Fill out the questionnaire and bring it to class on Friday.

Unfortunately, I can not respond individually to the reading assignments every day. I will, of course, respond to direct questions. There does not appear to be an easy way for me to automatically send you a "message received" note. Usually e-mail goes through fine, but sometimes messages do disappear without bouncing back to you. To be on the safe side, send yourself a copy every time you send me a response. Every now and then, ask me if there are any missing assignments, and if there are, forward your (dated) copy.

Due Monday 9/13 at 9am

Section 1.1 Functions All Around Us

• Be sure to understand: how a table can define a function, both examples

Section 1.2 Describing the Behavior of Functions

• Be sure to understand: what it means for a function to be increasing, decreasing, concave up, and concave down; what turning points and inflection points are.

E-mail Subject Line: Math 100 Your Name 9/13

1. Using the table on p. 4, estimate the time needed for a Trans Am to accelerate from 0 to 45 mph and from 0 to 75 mph. Which estimate do you think is more accurate, and why?
2. Does the table on p. 5 define the date as a function of the temperature? Why or why not?
3. Fig. 1.22 on p. 23 shows the height h of a ball, t seconds after it was tossed upward.
• Between what times is the height function h increasing?
• Between what times is the height function h concave up?

Reminder:

• If you need to retake the gateway, come talk to me about it, and perhaps retake it. No appointment is necessary to retake it, so drop on by, call to check whether I'm in, or come during office hours.
• The first problem set is due on Monday 9/20. You can find it at the bottom of the precalc web page.
• Remember that while you only need to turn in a few problems, you are responsible for all of those I assign.
• Begin working on the problems from sections we've covered now.

Due Wednesday 9/15 at 9am

Guidelines for Homework Presentation
Suggestions for Reading a Math Book
Section 1.2 Describing the Behavior of Functions

• Be sure to understand:Example on p. 12, periodic functions

E-mail Subject Line: Math 100 Your Name 9/15

1. Consider the function graphed in Fig. 1.23, on p. 24. For the following, estimate your answers as best you can.
• Identify the intervals where the function graphed in Fig 1.23 (p. 24) is decreasing.
• Identify the intervals where this same function is concave down.
• What are the turning points for this function?
• What are the inflection points?
2. Give an example of a real-life process which is periodic (other than those mentioned in the book.)
3. The weight of a package is related to the number of stamps needed to mail it.
• If you know the weight of the package, can you determine unambiguously the exact number of stamps needed to mail it? Use your answer to determine whether the number of stamps depends on the weight, and from there, conclude whether the number of stamps is a function of the weight.
• If you know the number of stamps needed to mail a package, can you determine unambiguously its weight? Use your answer to decide whether the weight depends on the number of stamps, and from there, conclude whether the weight is a function of the number of stamps.

Reminder:

• Retake the gateway if necessary
• Each week, behave as if the problem set is due on Friday. Have worked all the problems. Come to office hours! Bring any remaining questions to class on Fridays. The time between Friday and Monday is intended solely for getting the big picture and for nicely writing each problem to be turned in, complete with lucid and complete explanations.

Due Friday 9/17 at 9am

course policies (re-read, make sure all is clear & you're comfortable)
Section 1.3 Representing Functions Symbolically

• Be sure to understand: dependent and independent variables, domains and ranges

E-mail Subject Line: Math 100 Your Name 9/17

1. Consider the function
g(x)=1+(1/x) .

1. What is g(2)?
2. Is 0 in the domain?
3. Is 0 in the range?
2. Consider the formula for the volume V of a cube with side s, V=s3.
• Does the volume depend on the length of the side, or does the length of the side depend on the volume?
• Use your answer to determine whether V or s is the dependent variable. Which is the independent variable?
• Are the any values for s which do not make sense? How about for V? Use your answers to determine the domain and range for this function.
3. Is the time of high tide a function of the day of the year? (To avoid confusion, restrict yourselves to considering only one year.)

Reminder:

• Retake the gateway if necessary. The deadline for getting full credit is 9/22.
• Bring questions on PS 1 to class Friday
• Be sure to have worked on all the problems, not merely those to be turned in.

Due Monday 9/20 at 9am

Section 1.4 Connecting the Geometric and Symbolic Representations

• Be sure to understand:axes, ordered pairs, and how to plot points (I will not cover these). Determining whether a curve is a function, determining domain and range from a graph.

Section 1.5 Mathematical Models

• Be sure to understand:(I will not cover this section in class) mathematical models, interpolation, extrapolation

E-mail Subject Line: Math 100 Your Name 9/20

1. Find where the function
f(x)=x2+4
crosses the vertical axis. (Remember that the vertical axis is the line x=0.)
2. Consider the tossed ball whose height as a function of time is given on page 22, and which we see graphed in Figure 1.22 on page 23.
1. Is the point (3.3,40) on the curve shown in Figure 1.22?
Hint:Should you figure this out by looking at the graph, or might there be a better way?
2. For this same function, f(4)=0. What does this have to do with the graph? What does it have to do with the ball?
3. Must a mathematical model describe all aspects of the process it represents?
4. What is the difference between interpolation and extrapolation?

Reminders:

• The deadline for getting the full 100% on Gateway 1 is this Wednesday.
• Gateway 2 is this Thursday. Remember to sign up for a time to take it.

Due Wednesday 9/22 at 9am

At this point (8/24/99), this day is set aside for catching up or reviewing, if I feel we need it. However, if we can get ahead, that would be best, because there's some fun and challenging stuff ahead, and the more time we have to spend on it, the better.

Check back on 9/20 to see what I've decided you should do.

Here ends Chapter 1
Go to Chapter 2!

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 103
Norton, Massachusetts 02766-0930
TEL (508) 286-3970
FAX (508) 285-8278
jsklensk@wheatonma.edu

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