91Ó°ÊÓ

We have a finite domain and range, so we want to find all possible functions that map each element from the domain to an element in the range.

We will create tables for each possible function. A table will represent a function, and each entry will show the mapping of a domain element to a range element. 1. Function 1: \(-1 \mapsto -3\) \(0 \mapsto -3\) \(\pi \mapsto -3\) 2. Function 2: \(-1 \mapsto -3\) \(0 \mapsto -3\) \(\pi \mapsto \sqrt{2}\) 3. Function 3: \(-1 \mapsto -3\) \(0 \mapsto -3\) \(\pi \mapsto 5\) 4. Function 4: \(-1 \mapsto -3\) \(0 \mapsto \sqrt{2}\) \(\pi \mapsto -3\) 5. Function 5: \(-1 \mapsto -3\) \(0 \mapsto \sqrt{2}\) \(\pi \mapsto \sqrt{2}\) 6. Function 6: \(-1 \mapsto -3\) \(0 \mapsto \sqrt{2}\) \(\pi \mapsto 5\) 7. Function 7: \(-1 \mapsto -3\) \(0 \mapsto 5\) \(\pi \mapsto -3\) 8. Function 8: \(-1 \mapsto -3\) \(0 \mapsto 5\) \(\pi \mapsto \sqrt{2}\) 9. Function 9: \(-1 \mapsto -3\) \(0 \mapsto 5\) \(\pi \mapsto 5\) There are 9 different functions that can be formed with the given domain and range.

We have found all the possible functions (displayed as tables) whose domain is \(\\{-1, 0, \pi\\}\) and whose range is \(\\{-3, \sqrt{2}, 5\\}\). There are 9 possible functions in total.