how to write a function rule
To write a function rule, you need to follow these steps:
1. Identify the input (usually represented as x) and output (usually represented as y or f(x)) of the function.
2. Determine the relationship between the input and output. This can often be done by analyzing a table of values or a graph of the function. Look for patterns or trends in the data that can be described using mathematical operations.
3. Write the function rule as an equation that shows how the input (x) is transformed to produce the output (f(x) or y). The equation should include the operations and/or transformations needed to turn the input into the output.
4. Use function notation to represent the rule, that is, write f(x) = [equation] or y = [equation].
For example, let's say you have the following table of values for a function:
| x | f(x) |
|---|-----|
| 0 | 2 |
| 1 | 5 |
| 2 | 8 |
| 3 | 11 |
Notice that as the input x increases by 1, the output f(x) increases by 3. This suggests that the relationship between the input and output can be described by the equation:
f(x) = 3x + 2
This is the function rule that represents the relationship between the input x and the output f(x).