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 and b.

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?

b. inputs: social security numbers outputs: us citizens
is this relation a function?
is it a constant function?
is it a 1-1 function?

Explanation:

Part a

Is this relation a function?

Step1: Recall function definition

A relation is a function if each input has exactly one output. Each state (input) has exactly one governor (output).
So, the relation is a function.

Step2: Check constant function

A constant function has all outputs the same. Governors of states are different, so not constant.

Step3: Check 1 - 1 function

A 1 - 1 function has each output corresponding to exactly one input. Each governor corresponds to one state (since each state has one governor), so it is 1 - 1.

Step1: Recall function definition

A relation is a function if each input has exactly one output. A Social Security number (input) is assigned to exactly one US citizen (output), so it is a function.

Step2: Check constant function

A constant function has all outputs the same. US citizens are different, so not constant.

Step3: Check 1 - 1 function

A 1 - 1 function has each output corresponding to exactly one input. Each US citizen has exactly one Social Security number, so it is 1 - 1.

Answer:

s for part a:

• Is this relation a function? Yes
• Is it a constant function? No
• Is it a 1 - 1 function? Yes

Part b

Is this relation a function?