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


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)
=x(m - nx)

Profit Function

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

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