PA Chapter 8 Linear Functions

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Linear Functions

Relations

Any set of points.

Domain

The set of x-values.

Range

The set of y-values.

Input

Each domain value.

Output

Each range value.

Function

A relation with no repeating x-values such that there is exactly one output for each input.

Mapping Diagram

Lists the inputs and outputs in order drawing arrows from the inputs to their outputs.

Vertical Line Test

A visual test on a graph to determine if the relation is a function. If this line passes through more than one point, then it is not a function.

Vertical Line Equation

x = c

Horizontal Line Equation

y = c

Standard Form

ax + by = c

Slope-Intercept Form

y = mx + b

x-intercept

(x,0); The point which crosses the x-axis.

y-intercept

(0,y); The point which crosses the y-axis.

Increasing

A graph that rises from left to right.

Decreasing

A graph that falls from left to right.

Linear Function Graph

A function whose graph is a nonvertical line.

Nonlinear Function Graph

A function whose graph is not a line.

Slope

Rise/Run; Difference of the y-coordinates/Difference of the x-coordinates.

Positive Slope

An increasing line has this type of slope.

Negative Slope

A decreasing line has this type of slope.

Zero slope

A horizontal line has this type of slope.

Undefined Slope

A vertical line has this type of slope.

Same Slope

Parallel lines have this type of slope.

Opposite Reciprocal Slope

Perpendicular lines have this type of slope.

y-intercept

If a function is in the format y = mx + b, the b is the ___.

Direct Variation

Two points are in _____ if they relate to each other as y=kx.

Function Notation

Written as f(x), is read as "f of x", and represents the value of y given a value of x.

Systems of Linear Equations

Two or more linear equations.

Coordinate Point

A solution of a system is written as a _______ representing where the two lines cross.

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