16.5. Onto Functions

Try these first

1. 1.

   Define an onto function in your own words.

   Hint

   Think about functions where every output has a corresponding input.

2. 2.

   What condition must be met for a function to be considered onto?

   Hint

   Consider what it means for something to be covered completely.

3. 3.

   What is an onto function?

   • A function where not all outputs are covered
   • A function where every output is covered by at least one input
   • A function with no outputs

   Hint

   Remember the definition of mapping in functions.

4. 4.

   True or False: A function can be onto if the domain has fewer elements than the codomain.

   • True
   • False

   Hint

   Think about how functions work with outputs.

5. 5.

   Given a set A with 6 elements and set B with 4 elements, determine how many onto functions can exist.

   Hint

   Break it down using f(m, n) recursively.

6. 6.

   Explain why the number of onto functions decreases as the size of the codomain grows beyond the domain.

   Hint

   Think about coverage; if more elements exist in B than A, it can't map fully.