Functions Explained

What is a “Function”?

You put it exactly one color Here is a doughnut machine. of dough, it spits out exactly one kind of doughnut. DOUGH IN

This machine can only make a couple kinds of doughnuts, even though you put in all different colors of dough.

Two Flavor Doughnut Machine

Some machines only make one kind of doughnut, no matter the color you put in.

Bori ng Doughnut Machine

No matter what machine you use, ONE color dough should always make ONLY ONE type of doughnut!

• Seriously, what good is a doughnut machine if you have no idea what kind its gonna spit out????

 Same Dough…

Different Doughnuts???

BROK

Supe r C heap Jun k Doug hnut Mach in e

A FUNCTION is a type of math formula that You pick the X…. involves two variables, X and Y.

1 2 5 10 10 6 15 7 = x +

And the function produces a “Y” for each “X” you put in!

5

Sometimes a function is really boring.

34 64

2,135,789 y

2 2 = 2(0)x 2

+2

No matter what X you put in, the Y is always the same. This is called a “flat function”.

f(x) means “function of x”. It is used instead of y sometimes.

YOU get to pick whatever Let’s make a FUNCTION TABLE: Now, re-write figure the function with Y’s the ! Finally, out the

Okay, here’s our FUNCTION: X’s you want!!! X’s plugged in! EASY

x 0 1 2 3

f(x) = 2x + 1 y y = 2(0) + 1 y = 2(1) + 1 y = 2(2) + 1 y = 2(3) + 1

“Domain”

1 3 5 7

“Range”

Just like in an experiment, YOU control the DOMAIN (all the X’s)

And find out the RANGE (all the Y’s)

Write a function table for each function. You pick the X’s…figure out three Y’s for each function. 1. y = x + 5 2. y = 5x 3. y = x + 0

Just like the doughnut machine…. If different y’s come out

4 4 4

when using the same x, you know the function is BROKE!!!!

45 677 34 f(x) = ?????? NOT a function !!!!

x

Is it a function??

y

1

4

3

6

YES !

5

8

7

12

Is it a function??

(3,4)

(4,5)

Same x

(6,7)

(4,8)

Different y

BROKE ! ! Not a function !

The DOMAIN of a function is the group of X’s.

(4,5) (6,7) (1,3) The RANGE of a function is the group of Y’s that are produced.

REVIEW - y can be replaced with f(x) - the domain is the group of x’s - the range is the group of y’s - if an x has more than one y paired with it, then it’s NOT A FUNCTION. It is Broke!!