You can create functions that behave differently depending on the input (x) value.
Example: A function with three pieces:
- when x is less than 2, it gives x2,
- when x is exactly 2 it gives 6
- when x is more than 2 and less than or equal to 6 it gives the line 10-x
It looks like this:
(a solid dot means "including",
an open dot means "not including")
And this is how you write it:
The Domain is all Real Numbers up to and including 6:
Dom(f) = (-∞, 6] (using Interval Notation)
Dom(f) = {x 
| x ≤ 6} (using Set Builder Notation)
And here are some example values:
| X |
Y |
| -4 |
16 |
| -2 |
4 |
| 0 |
0 |
| 1 |
1 |
| 2 |
6 |
| 3 |
7 |
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