1.What's a function?

2.What's a domain?

4.Which of the following diagrams represent a function? Let \(X = { 1 , 2 , 3 , 4 }\) and \(Y = { a , b , c , d }\) .

5.Give a recursive definition for the following function: \(f : \mathbb{N} \rightarrow \mathbb{N}\) gives the number of snails in your terrarium \(n\) years after you built it, assuming you started with 3 snails and the number of snails doubles each year.

6.What is a surjective function?

7.What is an injective function?

8.When a function is both injective and surjective, it is called what?

9.Consider the function \(g : Z \rightarrow Z\) defined by \(g ( n ) = n^2 + 1\). Find \(g ( 1 )\) and \(g ( { 1 } )\) . Then find \(g^{−1}( 1 )\), \(g^{−1} ( 2 )\) , and \(g^{−1} ( 3 )\).