1. Bell Work InOut 49 712 1015 Find the pattern and fill in the numbers then write the function rule. Function rule: y= x + 5 1318 1621 1924

2. Function Rules

3. What is a function? It could be thought of as a Function Machine where certain inputs go in and certain outputs come out.

4. 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.

5. 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:

6. 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:

7. 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.

8. 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

9. Write a function rule for the input-output table. SOLUTION 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 Example:

10. 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 2 Write a function rule. Notice that each output value is twice the input value. So, a rule for the function is p = 2c. x2x2 x2x2 x2x2 x2x2 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.

11. 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

12. 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. -2

13. STEP 1 Find the value of a using STEP 2 Plug 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:

14. Write a function rule that relates x and y. SOLUTION 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 Function rule that relates x and y. 1 Let ( x, y )= ( 0, 5 ) 5 = 1 ( 0 )+ b, so b = 5 Example:

15. SOLUTION If you double the position number and subtract 3, you get the value of the term. So, the correct answer is B. +2 +1+1 +1+1 +1+1 +1+1 +1+1 2 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

16. Write a function rule that relates x and y. +1 +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 3 Function rule that relates x and y. Let ( x, y )= ( 1, 2 ) 2 = 1 ( 1 )+ b, so b = -1 YOU TRY!

17. 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 Function rule that relates x and y. Let ( x, y )= ( 1, -7 ) -7 = 1 ( 1 )+ b, so b = -8 +1

18. Practice: