Precalculus
• Course Contract
• Distance and standard equation of a circle:
• If A = (1,2) and B = (3,4). Can you find the standard equation of the circle which has AB as its diameter?
• Practice completing squares technique so you can convert a nonstandard equation to a standard equation.
• Example: Describe the figure: $2x2+ 2y2+ 3x - 5y + 1 = 0.$
• Write the equation of top half of the circle, which has center (1,1) and radius 3.
• If "sqrt" stands for square root, can you graph y = $sqrt\left(16-x2\right) + 3?$
• Line Equations
• 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 prduct weekly it has a cost of \$2 per unit, plus a fixed cost of \$1800. Each unit sells for \$5.

• (a) Find the cost, revenue and profit functions.
(b) Sketch these functions.
(c) Find the break-even point.
(d) Find the total weekly revenue at teh break-even point.
• Functions
1. Recall vertical line test, when will the graph represent a function?
2. 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.
• Higher Order Inequalities.
• Shifting and Reflection Techiques:
• Horizontal Shiftings: 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 Shiftings: 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).
• A Maple worksheet.
• A Java Applet
• Absolute value and the graphs  (Need to use ShockWave)
• Composite Functions and Inverse Functions