Question

relation
inverse
domain:
range:
is the original relation a function?
domain:
range:
is the inverse a function?
find t

Explanation:

Step1: Identify original domain

The domain is the set of input values (left oval): $\{-3, 0, 3\}$

Step2: Identify original range

The range is the set of output values (right oval): $\{0, 1, 2, 3\}$

Step3: Check if original is function

A function has each input mapping to one output. All inputs have one output: Yes

Step4: Define inverse relation

Swap input/output pairs: $(0,-3), (1,0), (2,3), (3,3)$

Step5: Identify inverse domain

Inverse domain is original range: $\{0, 1, 2, 3\}$

Step6: Identify inverse range

Inverse range is original domain: $\{-3, 0, 3\}$

Step7: Check if inverse is function

Each inverse input maps to one output: Yes

Answer:

Original Relation:

Domain: $\{-3, 0, 3\}$
Range: $\{0, 1, 2, 3\}$
Is the original relation a function? Yes

Inverse Relation:

Domain: $\{0, 1, 2, 3\}$
Range: $\{-3, 0, 3\}$
Is the inverse a function? Yes