Sept. 6 Class

Learning Goals: understand what a function is.

Today we began by talking about what is a relation.

    Relation: a set of ordered pairs.

In a way it, is a set of numbers that go together.  A function is a special kind of relation

    Function: a relation in which every "x" value has only one "y" value.

I demonstrated this by asking a few students to participate in a demonstration.  We had 3 students represent 'x' values and 3 students represent 'y' values.  In a function, every student who was an 'x' knew exactly which 'y' value they were partnered up with.  When a relation was not a function, we had an 'x' student who had multiple 'y' partners and was confused as to who they belonged with.

Then I showed some examples of mathematical relations that were functions or not functions.

Examples:

Mapping diagrams

The one on the left is a function.  The one on the right is not because x = 2 has two possible y values.

Ordered Pairs

(2, 4) (4, 8) (5, 10) (6, 12)  is a function

(2, 4) (2, 6) (3, 9) (4, 7) is not a function because the value of x = 2 is related two possible y values.

Graphs

Make sure you know the vertical line test!

Equations

y = x + 2    is a function (every 'x' gives one 'y' value).

y = ± x       is not a function (x = 1 can give y = +1 or y = -1)

For homework please work on P. 13 #1-16 (photocopied)