A. Definitions

relation  a set of ordered pairs of input and output values

domain  a set of input values, the xvalues, and the input variable (x) is the independent variable.

range  a set of output values, the yvalues, and the output variable (y) is the dependant variable

function  a relation that has exactly one output for each input OR one yvalue for each xvalue. The relation is not a function if an input value has more than one output.

function notation  f(x) = x^{2}  3x + 5 or g(x) = 2x + 6
B. Ways to Identify Functions

mapping  given a relation, match each xvalue with with its yvalue. If an xvalue gets "mapped" to more than one yvalue, then the relation is not a function. The relation {(3, 3) (1, 1) (4, 4) (1, 2)} is not a function because the xvalue 1 gets "mapped" to a yvalue of 1 and 2

vertical line test  a relation can be shown as a graph. If a vertical line touches the graph at exactly one point as it passes over the graph, then the relation is a function. A circle is not a function, but a parabola is a function.
C. Graphing Equations with One and Two Variables
 Graphing y = (any number)
 It's a horizontal line through that number on the yaxis.
 All points ont he horizontal line will have that same yvalue.
 Graphing x =(any number)
 It's a vertical line through that number on the xaxis.
 All points on the vertical line will have that same xvalue.
 Graphing an equation with x and y
 Construct a table of values, choosing at least 5 xvalues in the table.
 Substitute the xvalues into the equation to find the yvalues and to complete the table.
 Connect the points.
 If the connection makes a line, the equation is linear.
 If the connection makes a curve, the equation is NOT linear.
D. Evaluating Functions
 Substitute the given values in place of x.
 Follow order of operations to find the numerical value of the function.


