Notes, Lesson 2.4
Relations and Functions
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Definitions:
Relation ANY set of ordered pairs.
Domain The set of all x-coordinates in a relation. (independent variables)
Range The set of all y-coordinates in a relation. (dependent variables)
Mapping A pictoral matching up of domain elements with their corresponding range elements.
Function A relation where each element of the domain matches up with exactly one element of the range.
Vertical Line Test A test which takes a vertical line at any horizontal position. If at any position there is a crossing at more than one point, then the relation fails the Vertical Line Test, and the relation is not a function.
Identification. Is it a function? ... or not?
 
{(1,2),(2,3),(3,2)}
Function
This is a function because no x-coordinate has more than one y-coordinate matched with it.
y=3x-9
Function
This is a function because no x-coordinate will result in more than one y-coordinate.
Function
This is a function because no x-coordinate has more than one y-coordinate matched with it.
Function
The "Vertical Line Test" here shows that at no time will a vertical line ever cross the graph in more than one point. Therefore, this is a function.
{(1,2),(4,2),(6,4),(7,1),(1,3)}
Not a Function
Because of the two ordered pairs (1,2) and (1,3). There is a "violation." There is more than 1 y-coordinate for the x-coordinate 1.
Not a Function
Just one example of a "violation" is the pair of ordered pairs: (1,1), and (1,-1).
Not a Function
The two ordered pairs shown: (-3,9) and (7,9) violate the function rule.
Not a Function
The "Vertical Line Test" here shows more than 1 point of intersection. this shows that there is at least 1 pair of points with the same x-coordinate and a different y-coordinate. This is a violation of the Vertical Line Test. This is therefore not a function.
Function Notation:
f(3)
This is read "F of three"
Given f(x)=7x-2, find f(3). Sample Problem
f(3)=19
Substitute 3 in place of x in the given function f and calculate the result.
Given g(x)=7-2x, find g(-8) Sample Problem
g(-8)=23
Substitute -8 in place of x in the given function g and calculate the result.
Given h(x)=12x+9 find h(x+3) Sample Problem
h(x+3)=12(x+3)+9
Substitute (x+3) in place of x in the given function h.
h(x+3)=12x+36+9
Distributive Property
h(x+3)=12x+45
Simplify as much as possible.


Some Notes from Class


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