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 = $sqrt(16x2)\; +\; 3?$
 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 breakeven point.
(d) Find the total weekly revenue at teh breakeven point.
 Functions
 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.
 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