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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