Section 1.1: Functions

Point-by-Point Plotting

To sketch the graph of an equation:

1. Make a table of solutions - ordered pairs (x, y) of real numbers that satisfy the equation.
2. Plot these solutions as points in a rectangular coordinate system.
3. Connect the points with a smooth curve.

Example: y = x² - 4

x	-3	-2	-1	0	1	2	3
y	5	0	-3	-4	-3	0	5

Business Applications

Cost Function

A cost function describes the cost of making x items.

C	=	(fixed costs) + (variable costs)
	=	a + bx

Price-Demand Function

A price-demand function describes the number x of items that can be sold at $p per item.

p = m - nx

Revenue Function

A revenue function describes the total revenue from selling x items.

R	=	(number of items sold) × (price per item)
	=	xp
	=	x(m - nx)

Profit Function

A profit function describes the total profit from selling x items.

P	=	R - C
	=	x(m - nx) - (a + bx)