- Course Contract
- Quiz 1: January 22
- Note. When opening a math 'html' file in this web
page, it is preferable to use 'Internet Explorer'.
- Review on Pre-Calculus or College Algebra:
Exponents and Radicals
- page 0-18:,31,33,35,37,39.
- page 0-24: Odd numbers, 1-7,19-49.
- Practices on factorings
- Exercises on Quadratic Equations.
- More Exercises on Factorings (added on January 12/07).
- page 0-32: 13,15,17,19.
- Exercise on solving absolute value inequalities.
- More exercises on Linear Inequalities and Absolute Value Inequalities.
- Solving Quadratic Inequalities
- Standard Equation of a circle:
- Word Problems: Break Even Analysis, Rental Car Problem and etc.
- Example: You are about to take a trip and you plan to rent a car, here are two rental offers: (i) Hertz will give you 30 cents per mile and $45 per day, and (ii) Avis will give you 25 cents per mile and $50 per day. Suppose you decide to rent a car for 4 days. Which company offers you a better deal? Explain. Answer.
- Example A manufacturer of electronic
components finds that in making x units of a product weekly it has a
cost of $2 per unit, plus a fixed cost of $1800. Each unit sells for $5.
- Find the cost, revenue and profit functions.
- Sketch these functions.
- Find the break-even point.
- Practice Problems
- Recall vertical line test, when will the graph represent a function?
- Domain and Range:
(a) When you know the graph of a function, you can tell what the domain (inputs or x) and range (outputs or y) are.
- Drills on finding the domain of a function.
- Shifting and Reflection Techniques:
- Horizontal Shifting: y = f(x + a) is a horizontal shifting of y = f(x). If a > 0, then the graph will be shifted to the left; if a <0, then the graph will be shifted to the right.
- Vertical Shifting: y = f(x) + a is a vertical shifting of y = f(x). If a > 0, then the graph will be shifted up; if a <0, then the graph will be shifted down.
- y = - f(x) is a reflection of y = f(x).
- Drill (Do only the first two exercises, skip the trig functions).
- Exercises from pages 69-70: #1 through 25 odd; 49, 50.
- Open box problem: An open box is to be made from a 16 in. by 30 in. piece of cardboards by cutting out squares of equal size from the four corners and bending up the sides. What size should the squares be to obtain a box with largest possible volume?