Name_________________________________________
Date___________
Teacher _______________________________________
Per.___________
What would it mean for two Pepsi Machines to be the same?
A function is like a Pepsi® machine, you put something into it and you get something
out. We are going to look at functions represented in three ways: Words, Graphs, and
Symbols.
FUNCTIONS USING WORDS
[1] In terms of money, what would it mean for two PEPSI machines to be the SAME if
you wanted one soda? Write your answer. [Make up a price for one Pepsi. Now if two
machines were the SAME, what would that mean if you wanted a soda from either one of
them?]
[2] What if you wanted two sodas, what would it mean for two PEPSI machines to be the
SAME?
[3] What if you wanted three sodas, what would it mean for two PEPSI machines to be
the SAME?
FUNCTIONS USING GRAPHS:
For graphs, the stuff you “drop in” to a function goes on the horizontal axis. The stuff
that comes out is plotted vertically.
Just look and turn to next page.
Shown below is a graph of a PEPSI machine (the Pepsi machine function) that charges
$0.75 for each can. You have to put in $0.75 to get one Pepsi. You have to put in $1.50
to get two Pepsi’s.
[4] On an axis, draw the graph for a second Pepsi Machine that is the SAME as the first
Pepsi machine.
So far we’ve used WORDS and GRAPHS to talk about functions. Now we are going to
look at some SYMBOLS to represent functions. We’ll be using the graphs as a way to
make sense of the symbols.
The Graphing Calculator
Before starting, there are just a couple of little things you should know (then go to Step 1):
I. If (when?) you get lost in using the calculator, DON’T worry!
Just push the follow sequence
2nd (yellow button) then Mode (really Quit)
until you get to a blank screen. (You may need to press
CLEAR to get a completely blank screen).
II. As you will see, the arrow keys allow you to “drive around the screen”.
================ Let’s Get Started ================
Step 1: Turn ON the Calculator. [Lowest and Left-most button].
[To turn it OFF when you are done, press 2nd (yellow button) then ON]
Step 2:
Step 3:
Press the yellow button, 2nd, and then the MODE button which is next to
the yellow second button.
Press CLEAR (under the arrows).
Now we are going to enter some functions into the calculator.
Step 4: Clear all the functions then type in:
Y1=x+2
Y2=2x
Y3=4sin(x)
Y4=-x
You should see
.
The short cut for X is the X,T key. Make sure your use the negative button (-) which is
the GRAY button next to Enter. On –x.
Step 5: Now press GRAPH (top row, right-most button).
Step 6: Sketch what you see. You’ve entered and graphed four functions!
Your teacher will now collect everyone’s Y1-Y4
Sketch what you see upfront.
Why don’t you see more lines?
What does it mean on a GRAPH for TWO FUNCTIONS to be the
SAME? Write your answer:
Challenge 1:
Step 1: Press Y= again. Then Press CLEAR. Press the down arrow and then press
CLEAR do this for all of the funtions. Now press the up arrow until you’re at the Y1=
location.
Step 2: Type in 4x
See:
[to do this Press the number 4 then X,T; ENTER].
Y1=4x
[the other lines should be blank]
Step 3: Press GRAPH.
Sketch what you get.
Step 4: Make up and type in any three functions of your own (anything you want).
Examples:
Pressing X,T + 3 will give you x+3
==> Press ENTER.
Pressing 4 sin X,T ) will give you 4sin(x)==> Press ENTER.
Pressing 3 X,T + 2 will give you 3x+2 ==> Press ENTER.
Step 5: Press GRAPH.
Draw what you get and label each line with which function it is (e.g. x+3)
The teacher will now collect all of your functions. What do you see upfront?
Challenge 2: Find five functions that are the SAME as
4x
(At Y1= press 4 then X,T then ENTER)
Example: Try 2x + 2x (Drive to Y2= , Press 2
then X,T then + 2 followed by X,T then ENTER).
See:
Y1 = 4x
Y2= 2x+2x (<== If you think of another, type it here instead
of this one. Write it down if it works).
How will you know if your functions are the SAME as 4x?
Press GRAPH. [Now try to find five of your own that are the same as 4x].
Write down the five functions that are the same as 4x. You should write them down as
you find them:
1.
2.
3.
4.
5.
6. Write down your strategy for figuring out functions which would be the same as 4x?
7. Go to the activity center, and type in your favorite function from the your list above.
Challenge 3: Find five functions that are the SAME as
4sin x
(Press Y=. At Y1= press 4
then sin then X,T then ) ;
now press ENTER)
Example: Try 2sinx + 2sinx (Drive to Y2= , Press 2 then sin then
X,T and ). Now press + then 2 then sin then
X,Tand ) then ENTER).
Y1 = 4sin(x)
Y2 = 2sin(x) + 2sin(x)
Press GRAPH.
As you find them, write down five functions that are the same as 4sin(x):
1
;
2.
3.
4.
5.
6. Write down your strategy for figuring out functions which would be the same as 4sin
x?
7. Go to the activity center, and type in your favorite function from the your list above.