Function Notation f(x)

f(x)=3x+4

"f of x equals 3x+4"

We know this is a function based on the notation.**The mathematician is telling you that they are functions.

f(x)=3x+4
g(x)=2x+5

The g means that they are both functions.

f(2)  What do you think this means?

This means that x is equal to 2.

f(x)= 3x+4
f(2)=?

Same as   y=3x+4; x=2

y=3(2)+4=10

R-13 Definition of a Function with examples

A function is a set of ordered pairs (x,y) where each x has only one y associated with it.

Non-Function
x  y
0  1
1  2
1  3
2  4


Function
x  y
0  2
1  4
2  6
3  8

x  y
0  1
1  2
1  2
2  3
3  4

**This is a function because x only has one y associated with it.

Relation:Simply a set of ordered pairs. (x,y) coordinate pairs.

**Everything is a relation, some few collect things are a function.


Can be a function, but doesn't have to be. If it is a function, it can be a relationship.

A relation can be a non-function.

Family example:  Mrs.O'Toole has a relation with her daughter and son. It is a family relationship.
Mrs.O'Toole has a relation with Lauren, but with her family it is a special relation.

Question: Is every Linear Relationship a function?

yes? no? Justify it mathematically.

NO

Line of best fit.
vertical lines. x=4

Functions and Non-Functions

Math Merge Seminar 1:Task

What observations can we make?

Graph Part

Non-Function
-symmetrical with x-axis
-seemed to have some closing points


Function
-symmetrical with y-axis
-seemed to have symmetry
-Go one way on the x-axis
(Don't go and come back)

What are some generalizations we can make about symmetry and how the symmetry is different for a non-function vs. a function?

Table Part

Non-Function



Function


Do you think you could draw a graph and be fairly confident it is a function? a non-function?

The class is still in disequilibrium of the meaning of a function.

Looking at the tables of functions and non-functions, what observations can you make?


Equation Part

Function
-Doesn't have a y^2
-2 or more variables


Non-Function
-Has a y^2
-2 or less variables

R-9 Terminating and Repeating Decimal

What is a terminating and repeating decimal?

Terminating: 
1.5, 1.75, 1.4

Repeating: 
Decimal that just keeps repeating the same #'s.
ex. 1.33 or 1.333333
A set of #'s that repeats
ex. .xyxyxyxy



What happens when decimals keep changing?

Fraction	Equivalent Fraction with 10, 100, 1000, etc in the denominator	Decimal	Identify as Terminating or Repeating
2/5	4/10	.4	Terminating
3/8	375/1000	.375	Term
5/6	833/1000 (Class still not sure)	.8333333	Repeating
35/10	35/10	3.5	Terminating
8/99	80.80/1000	.080808	Repeating

R-10 Make 5-7 observations about this chart