Function as Mapping Math Example 1

Solution

1. 1
   A function requires every element of the domain to map to exactly one element of the codomain. Check: $f(1)=a$, $f(2)=a$, $f(3)=c$ — each domain element has exactly one image. ✓ Valid function.
2. 2
   The range is the set of actual output values: $\{a, c\}$ (note $b$ is in the codomain but not in the range).
3. 3
   Observe this is many-to-one: both $1$ and $2$ map to $a$.