The completed table for the function Y = 3x - 5 confirms a consistent pattern, where each input value (x) corresponds to the correct output (y). This supports the validity of the function rule, demonstrating its application across various input values.
To complete the table for the given function rule Y = 3x - 5, we can substitute each value of x into the function to find the corresponding y-values:
| x | y |
|----|----|
| -6 | -23|
| -3 | -14|
| 0 | -5 |
| 3 | 4 |
| 6 | 13 |
Here's how the table is filled in:
| x | y |
|----|------------------------|
| -6 | (3 * -6) - 5 = -18 - 5 = -23 |
| -3 | (3 * -3) - 5 = -9 - 5 = -14 |
| 0 | (3 * 0) - 5 = 0 - 5 = -5 |
| 3 | (3 * 3) - 5 = 9 - 5 = 4 |
| 6 | (3 * 6) - 5 = 18 - 5 = 13 |
So, the completed table is as follows:
| x | y |
|----|----|
| -6 | -23|
| -3 | -14|
| 0 | -5 |
| 3 | 4 |
| 6 | 13 |
In words, when the input (x) is -6, the output (y) is -23. Similarly, when x is -3, y is -14; when x is 0, y is -5; when x is 3, y is 4; and when x is 6, y is 13. The pattern is consistent with the given function rule Y = 3x - 5.