To sketch the graph of an equation:

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

x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
---|---|---|---|---|---|---|---|

y | 5 | 0 | -3 | -4 | -3 | 0 | 5 |

A **cost function** describes the cost of making *x* items.

C | = | (fixed costs) + (variable costs) |

= | a + bx |

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

p = m - nx

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

R | = | (number of items sold) × (price per item) |

= | xp | |

= | x(m - nx) |

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

P | = | R - C |

= | x(m - nx) - (a + bx) |