Relations & Functions
A relationship can be shown between numbers in several ways: table of values, equation, graph, words, mappings.
The first variable in a relation is called the independent variable.
The second variable is the dependent variable.
Domain – the set of values for which the independent variable is defined.
Range – the set of values of the dependent variable (determined by the values in the domain)
Function- a relation in which there is only one value of the dependent variable for each value of the independent variable.
How do we tell if a relation is a function? One way….
The vertical line test (VLT)
This is a function since the VL passes through one point.
This relation is not a function since the VL goes through two points.
This relation is not a function since the VL goes through two points
For each of the following relations, determine
- domain & range
- whether or not it is a function
1) {(1,2), (2,3), (3,5), (4,7)}
a) Domain ={1,2,3,4}
Range={2,3,5,7}
b) This relation is a function by the VLT
2) y=x2
x:-2,-1,0,1,2
y:4,1,0,1,4
a) Domain ={ x∈R }
{the set of real numbers}
Range = {y∈R,y≥0}
a) Domain ={ x∈R,-4≤x≤4 }
Range = {y∈R ,-4≤y≤4 }
b) This is not a function by the VLT.
(for any value of x, there are two values of y)
Mapping Notation
a) Domain ={1,2,3,4}
Range={2,3,5,7}
{(2,1),(2,3),(3,5),(4,5), (5,7)}
This relation is not a function since there two possible values of y (y=18, y=3) when x=2
