- 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:
- 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 =
- 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.
Shifting and Reflection Techiques:
- 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.
Composite Functions and Inverse Functions
- 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.
value and the graphs (Need to use ShockWave)