To fill a table using a function rule, you substitute each input value (usually represented by 'x') into the function, perform the calculation as defined by the function rule, and then record the resulting output value (usually represented by 'y').
Here's a breakdown of the process:
-
Understand the Function Rule: The function rule is an equation that defines the relationship between the input (x) and the output (y). For example:
y = x + 4. -
Identify the Input Values: The table will provide a set of input values (x-values) that you need to use.
-
Substitute and Calculate: For each input value, substitute it into the function rule in place of 'x'. Then, perform the calculation to find the corresponding output value ('y').
-
Record the Output Value: Write the calculated output value ('y') in the table next to its corresponding input value ('x').
Example:
Let's say we have the function rule: y = x + 4 and the following table:
| x | y |
|---|---|
| -10 | |
| -9 | |
| -8 |
Here's how we'd fill in the 'y' values:
- For x = -10:
y = -10 + 4 = -6 - For x = -9:
y = -9 + 4 = -5 - For x = -8:
y = -8 + 4 = -4
The completed table would look like this:
| x | y |
|---|---|
| -10 | -6 |
| -9 | -5 |
| -8 | -4 |
In summary, filling a table with a function rule involves substituting the given input values into the function, calculating the corresponding output values, and then recording these values in the table.
