1. Writing Function Rules
Lesson 23
Introductory Algebra
Writing Function Rules

2. Warm-Up Complete the following input-output table. Input x
Function Rule
y = 6x
Output y 1 2 3
Input x
Function Rule
y = 4x – 2
Output y 2 3 5 8

3. Writing Function Rules
Target:
Write function rules for tables or graphs.

6. Vocabulary
Start Value: The output value that is paired with the input value of zero.

7. Writing Function Rules From Tables and Graphs
If given a graph, create an input-output table using the ordered pairs of the points on the graph.
Make sure the input column starts at zero and counts up by one.
Determine the start value (the output number paired with an input value of zero).
Determine the amount of change (amount the output numbers are increasing/decreasing by).
Write the function rule by filling in the start value, operation and amount of change.
y = __ ± __ x

8. Example 1 Find the function rule for the input-output table.
The input column starts at 0 and counts up by one.
The start value is 2.
The amount of change is increasing
by 3.
The function rule is: y = 2 + 3x
Input x
Output y 2 1 5 8 3 11

9. Example 2 Find the function rule for the graph.
Create an input-output table.
Start Value: 10
Amount of Change: – 2
Function Rule: y = 10 – 2x
Input x
Output y 10 1 8 2 6 3 4 5

10. Exit Problems Find the function rule for the table.
Input
Output 3 1 8 2 13 18 4 23
Find the function rule for the table.
Find the function rule for the graph.

11. Communication Prompt
What are the four ways of representing a function? Which do you think is most useful and why?