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# c h a p t e r o n e

### Functions

Question | Answer |
---|---|

variable | symbol that can be replaced by any member of a set of numbers or objects |

algebraic expression | The result when numbers and variables are combined using the operations of arithmetic. |

Order of Operations | 1. Perform operations in parentheses, brackets. 2. Take powers. 3. Multiply and divide in order from left to right 4. add and subtract in order from left to right. |

What is the dependent variable in the equation P=5H and why? | P because its value depends on the amount for H. (H is independent variable) |

Function | A correspondence or pairing between 2 variables such that each value of the first (independent) variable corresponds to exactly one value of the second(dependent) variable. |

Range of a Function | The set of values of the dependent variable that can result from the substitutions for the independent variable. |

Domain of a function | the set of values which are allowable substitutions for the independent variable |

How is f(x) read? | "f of x" |

How is T:x--> x read? | "T maps x onto x." (arrow notation) |

Theorem (Vertical-Line Test for Functions) | No vertical line intersects the graph of a function in more than one point. |

How do you "clear" an equation of fractions? | Multiply each side of the equation by a common multiple of the denominator. |

How do you simplify equation d= rt? | multiply both sides by r. d/r = rt/r. Simplify d/r = t. |

What is an explicit formula for the nth term of the sequence 1, 3, 6, 10, 15, 21, . . . ? | t(n) = n(n+1)/2 |

What does a recursive formula state? | a. The first term b. tells how the nth term is related to one or more of the previous terms. |

What are explicit formulas good for that recursive formulas are not? | Explicit formulas help to find an answer for a large integer. |

What are recursive formulas good for that explicit formulas are not? | Recursive formulas help to find a series of numbers. |

Created by:
katelesperance