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MTH403A: Functions

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

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