How do I make a table for f(x)= [[x-1]] ? It's a greatest integer function..
To make a table for the function f(x) = [[x-1]], where [[x-1]] represents the greatest integer less than or equal to (x-1), you can follow these steps:
1. Choose a range for the variable x that you want to evaluate the function within. For simplicity, let's say we choose a range from x = -5 to x = 5.
2. Create a column for the values of x and another column for the corresponding values of f(x).
3. Start by evaluating the function for the lowest value of x in your chosen range. In this case, it is x = -5. Substitute -5 into the function: f(-5) = [[-5-1]].
4. Calculate the value of [[-5-1]]. Since -6 is the greatest integer less than or equal to -5-1, [[-5-1]] = -6.
5. Fill in the first row of the table with the values: x = -5 and f(x) = -6.
6. Repeat steps 3-5 for each value of x within the chosen range, incrementing x by 1 each time until you reach the highest value. In this case, you will evaluate f(x) for x = -4, -3, -2, -1, 0, 1, 2, 3, 4, and 5.
Here is the completed table:
| x | f(x) |
|-------|---------|
| -5 | -6 |
| -4 | -5 |
| -3 | -4 |
| -2 | -3 |
| -1 | -2 |
| 0 | -1 |
| 1 | 0 |
| 2 | 1 |
| 3 | 2 |
| 4 | 3 |
| 5 | 4 |
Please note that the greatest integer function only returns whole numbers (integers), as it rounds down to the nearest integer.