Unit 6 - Functions

Continuous Whole

A Continuous Whole means that we go from one point to another without a break

Discrete Unit

A Discrete Unit is indivisible. What does this mean? If it is divided then what result will not exist. Example: Half a person is NOT a person.

Linear Function

A function that creates a straight line; a function with a constant slope

Nonlinear Function

A function that does not create a straight line; often graphed as a curve

Rate of Change

A ration that shows how one variable changes with respect to another. On a linear graph, this is called the slope of the line.

Function

A relation is a function if each x-value is paired with one and only one y-value; "X's don't repeat"

Relation

A set of ordered pairs; Example: (6, 2), (5, -1), (0, 6), (-4, 1); Can be shown as: ordered pairs, tables, graphs

Equations as Functions (1 of 2)

Functions can also be represented by an equation (or rule). The equation will generate ordered pairs by taking an input (x) that results in a certain output (y).

Vertical Line Test

If any vertical line passes through the graph of a relation no more than once, then its a function

Perpendicular Lines

Line that intersect at a 90 degree angle. They have negative (opposite) reciprocal slopes.

Parallel Lines

Line that never intersect. They have a same slope.

Types of Slope

Position, Negative, Zero, and Undefined

Slope

Slope is written as a ratio of the vertical change (rise) to the horizontal change (run) between any two points on a line. This remains constant for any two points on the same line. Slope is written as a fraction in simplest form Variable for slope: m

Domain

The set of x-values within a relation

Range

The set of y-values within a relation

Equations as Functions (2 of 2)

The x-value is always called the independent variable. The y-value is always called the dependent variable. The graph of an equation is the set of all its ordered pairs, which often form a line or curve.