Function rules and Other Cool Math Stuff
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Transcript Function rules and Other Cool Math Stuff
Function Rules from Tables
There are two ways to
write a function rule
for a table
The first is through
number sense (this
involves guessingand-checking
Function Rule
Try
adding/multiplying the
X by some number to
see if you can get Y
You can also try
adding/subtracting
after you multiply
Function Rule
We can see the
equation will be
Y = 3x +2
Function Rule
The second method works
in the X values are
consecutive (ex. 1, 2, 3)
If they are, we can take
the difference of the Y
values (ex. 5-2 = 3)
That result will be to
coefficient for X (ex. Y =
3x)
Now we will determine if
we have to add/subtract a
constant
Mrs. Vanderbilt's Lawn
We have been hired to mow Mrs.
Vanderbilt's lawn. She is going to give us a
two dollar bonus for starting early. In
addition to this she will pay us 3 dollars an
hour.
What is the function rule for this problem?
Writing Tables from Function
Rules
Since 2 dollars is a
bonus, we get that as
soon as we start. We
get 3 dollars an hour
after that.
Y=3x+2
First we can choose
any values for x we
want unless they are
given to us.
Tables From Function Rules
The next step is to
plug these values in
for the variable x in
our equation.
Y=3x+2
Y=3(0)+2
Y=2
Tables From Function Rules
Now let’s try the next
set of numbers.
y=3(1)+2
y=5
Tables from Function Rules
As you plug in the rest
of the values for x,
you will get the
corresponding values
for y.
Graphing Tables and Function
Rules
First of all if you only
have a function rule
you need to make a
table which we just
covered.
From the table to the
left we make a graph
Mrs. Vanderbilt's Lawn
We will need to plot
the set of numbers as
they as they appear in
the table.
For the first set of
numbers we will go 0
to the right and up 2
For the next set of
numbers we will go 1
to the right and 5 up
Mrs. Vanderbilt's Lawn
Mowing Lawns
y-axis (dollars)
Of course this is just
the first two sets of
numbers.
Let’s see what
happens if we plot the
rest of the numbers
16
12
8
4
0
0
1
2
3
x-axis (hours)
4
5
Mrs. Vanderbilt's Lawn
After plotting all the
points we can draw a
line from point to
point that will help us
find values between
the points.
Mowing Lawns
y-axis (dollars)
16
12
8
4
0
0
1
2
3
x-axis (hours)
4
5
Mrs. Vanderbilt's Lawn
Using the line we can
tell how much money
we can make mowing
her lawn for 2 and a
half hours or or four
and a half
Mowing Lawns
y-axis (dollars)
16
12
8
4
0
0
1
2
3
x-axis (hours)
4
5