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# MTH403A: Functions

### The Unit Review of Unit 1: Functions, Precalculus/Trigonometry.

Term | Definition |
---|---|

Dependent variable | A variable in a function whose value is dependent upon the value of the independent variable. |

Independent variable | The input variable in a function. Its value determines the value of the dependent variable. |

Function | A special kind of relation in which each value of the input variable is paired with exactly one value of the output variable. A function usually has form of 'f(x) = x'. |

Domain | The set of all possible values of the independent variable. It is also the set of all values a function takes as inputs. The domain is represented by 'x'. |

Range | The set of all possible values of the dependent variable. It is also the set of all values a function returns as outputs. Range can be noted as 'f(x)', or 'y'. |

Interval Notation | A shorthand way of writing intervals using parentheses and brackets. Parentheses signify EXCLUDED value, while Brackets signify INCLUDED value. |

Absolute Value function | f(x) = |x|. The magnitude of x. |

Greatest Integer function | f(x) = x. The greatest integer less than or equal to x. |

Many-to-One | A function where two or more x-values are assigned to one y-value. |

One-to-One | A function where each y-value has one assigned x-value. |

Vertical Line Test | A vertical line drawn through a graph will touch in, at most, one place. Otherwise the test is failed, and the graph is not a function. |

Difference Quotient | A method of finding the slope between two points on a curve. |

Linear function | A function whose graph is a line. |

Slope | A ratio of the increase in y-coordinate of a line to the increase in x-coordinate of that line. |

Arithmetic Sequence | A collection of number separated by commas in which the difference between any two adjacent numbers is constant. |

Explicit Formula | A formula that allows the direct calculation of all terms in a sequence. |

Partial Sum | The sum of the first 'n' terms of a sequence. Denoted by the symbol Sn. |

Recursive Formula | A formula that defines numbers in a sequence in terms of previous numbers in the sequence. |

Sequence | A set of numbers written in a particular order. |

Series | A collection of terms in a sequence that are added together to produce a sum |

Sigma Notation | A shorthand notation using the Greek letter 'sigma' to denote the sum of a series. |

Linear Equation | An equation in which the variable is of degree one. |

Linear Inequality | An inequality in which the variable is of degree one. |

Point-Slope Form | A form of a linear equation that includes the coordinates of a point on the line and the line's slope. y – y1 = m(x – x1); (x1, y1) |

Slope-Intercept Form | A form of a linear equation that includes the slope of the line and the value of the y-intercept. y = mx + b |

Standard Form (of a Linear Equation) | A linear equation written in the form Ax + By + C = 0. |

Undefined | A value that cannot be computed. |

Coincide | To overlap, or in the case of lines, be identical. |

Feasible Region | A region on a graph that includes all possible solutions to a system of inequalities. |

Matrix | A collection of numbers represented in a rectangular format |

Matrix Algebra | A set of rules that describe how to solve complex algebraic problems using matrices. |

Ordered Pair | A combination of x- and y-coordinates that describe a point on a graph. (x, y) |

Parallel Lines | Two lines with equal slopes that never intersect. |

System of Linear Equations | A set of two or more linear equations. |

Commutative Property | Operations may be performed in any order and they will always produce the same result. |

Function Composition | Combining two functions into a single function. |

Created by:
TeralynE