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30 terms

PA Chapter 8 Linear Functions

Linear Functions
STUDY
PLAY
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.