Question

which of the following relationships are functions? for each one answer \yes\ if it is a function and
o\ if not a function. if it is a function then answer yes/no to the additional questions. answer parts a through e
is it a constant function?
is it a 1-1 function?
a. inputs: states outputs: governors
is this relation a function?
is it a constant function?
is it a 1-1 function?

Explanation:

Part a: Inputs - States, Outputs - Governors

1. Is this relation a function?

A relation is a function if each input (state) has exactly one output (governor). In the real world, each state has only one governor at a time. So, each input (state) maps to exactly one output (governor).

A constant function is a function where every input maps to the same output. Since different states have different governors (outputs), the output is not the same for all inputs.

A one - to - one (1 - 1) function is a function where each output is mapped to by exactly one input. Since different states (inputs) have different governors (outputs) (and we assume no two states have the same governor at the same time), each output (governor) is associated with exactly one input (state).

Answer:

Yes

2. Is it a constant function?