Bell Work InOut 49 712 1015 Find the pattern and fill in the numbers then write the function rule....
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Transcript of Bell Work InOut 49 712 1015 Find the pattern and fill in the numbers then write the function rule....
Bell Work
In Out
4 97 12
10 15
Find the pattern and fill in the numbers then write the function rule.
Function rule: y= x + 5
13 1816 2119 24
Function Rules
What is a function?
It could be thought of as a Function Machine where certain inputs go in and certain outputs come out.
Suppose we put some numbers in our Function Machine and certain numbers come out.
3 ,
5 ,
4 ,
5 ,
6
6 ,
7 ,
8
Do you see a pattern between the inputs and outputs?Pattern: Add 2 to the input to get the output.
Predict what will happen when we put 10 in our Function Machine.
3 ,
5 ,
4 ,
5 ,
6,…
6 ,
7 ,
8,…
12
10
Pattern: Add 2 to the input to get the output.
REMINDER:
Predict what number must be put in our Function Machine to get an output of 15.
3 ,
5 ,
4 ,
5 ,
6,…
6 ,
7 ,
8,…,
12,
10,
15
13
Pattern: Add 2 to the input to get the output.
REMINDER:
What is the function of this machine?
3 ,
5 ,
4 ,
5 ,
6,…,
6 ,
7 ,
8,…,
12,
10,
15
13
+ 2
We can write this as a function rule:y = x + 2, x is the input and y is the output.
Writing a Function Rule
Write a function rule for the input-output table.
SOLUTION
What is the pattern?
A function rule for the input-output table is y = x + 2.5.
ANSWER
Add 2.5 to each input x to get the output y.
What is the function rule?
y = x + 2.5
+2.5+2.5+2.5+2.5+2.5+2.5+2.5
Write a function rule for the input-output table.SOLUTION
5xy
What is the pattern?Add 5 to each input x to get the output y.
What is the function rule?
A function rule for the input-output table is y = x + 5.
ANSWER
+5
+5
+5
+5
+5
Example:
Making Cuts
In the cheese-slicing diagram below, the input c is the number of cuts made across the center of the cheese, and the output p is the resulting total number of pieces of cheese. Write a rule for the function. Then use the rule to find the number of pieces made with 9 cuts.
STEP 1
Make an input-output table.
STEP 2Write a function rule. Notice that each output value is twice the input value. So, a rule for the function is p = 2c.
x 2
x 2
x 2
x 2
STEP 3
p = 2(9)
p = 18
So there are 18 pieces made with 9 cuts.
Evaluate the function when c = 9 to find the number of pieces made with 9 cuts.
Write a function rule for the input-output table. Then use the rule to find the output y when x = 12.
You Try:
SOLUTION
What is the pattern?
Subtract 3 to each input x to get the output y.
What is the function rule?
y = x - 3
y = x – 3 Write original equation.
y = 12 – 3 Substitute x = 12
y = 9 Simplify.
-3 -3 -3 -3
Write a function rule for the input-output table. Then use the rule to find the output y when x = 12.
YOU TRY!
SOLUTION
What is the pattern?
Divide each input x by -2 to get the output y.
What is the function rule?
Write original equation.
Substitute x = 12
Simplify.
2x
y
2
12
y
6y
2x
y
-2
STEP 1Find the value of a usinginputin change
outputin changea
STEP 2Plug a into the equation y = ax + b.
To find b, substitute an input-output pair for x and y.
STEP 3
STEP 4 Plug value of b into the equation y = ax + b to obtain the function rule.
Sometimes we can’t see the pattern right away.
4 Steps for writing a function rule:
Write a function rule that relates x and y.SOLUTION
Find the value of a.
Plug value of a into y = ax + bFind b by substituting an input-output pair for x and y.
Plug value of b into y = ax + b
bxy 1
5xy
Function rule that relates x and y.
2
2
inputin change
outputin changea 1
Let (x, y)= (0, 5)
5 = 1(0)+ b, so b = 5
Example:
SOLUTION
If you double the position number and subtract 3, you get the value of the term. So, the correct answer is B.
+2
+2
+2
+2
+2
+1
+1
+1
+1
+1
1
2
inputin change
outputin changea
bxy 2
2
32 xy
Find the value of a.
Plug value of a into y = ax + b
Find b by substituting an input-output pair for x and y.
Plug value of b into y = ax + b
Let (x, y)= (2, 1)
1 = 2(2)+ b, so b = -3
ANSWER
Write a function rule that relates x and y.+1 +1 +1 +1
+3 +3 +3 +3
Find the value of a.
Plug value of a into y = ax + b
Find b by substituting an input-output pair for x and y.
Plug value of b into y = ax + b
1
3
inputin change
outputin changea
bxy 3
13 xy
3
Function rule that relates x and y.
Let (x, y)= (1, 2)
2 = 1(1)+ b, so b = -1
YOU TRY!
Write a function rule that relates x and y in the table at the right.
SOLUTION
You Try!
Find the value of a.
Plug value of a into y = ax + b
Find b by substituting an input-output pair for x and y.
Plug value of b into y = ax + b
1
1
inputin change
outputin changea
bxy 1
8xy
1
Function rule that relates x and y.
Let (x, y)= (1, -7)
-7 = 1(1)+ b, so b = -8
+1 +1 +1
+1 +1 +1
Practice: