Question

a. function
domain: {alice, brad, carl}
range: {cat, dog}

b. function
domain: {cat, dog}
range: {alice, brad, carl}

c. not a function

Explanation:

Analyze the mapping diagram

Using the Relation Mapping knowledge point, we identify the inputs and outputs from the diagram:

• Input "Alice" maps to output "cat".
• Input "Brad" maps to output "dog".
• Input "Carl" maps to output "dog".

Determine if the relation is a function

Using the Definition of a Function knowledge point, we check if each input in the domain maps to exactly one output in the codomain.

• "Alice" maps to exactly one element ("cat").
• "Brad" maps to exactly one element ("dog").
• "Carl" maps to exactly one element ("dog").

Since every input maps to exactly one output, this relation is a function.

Identify the domain and range

Using the Domain and Range knowledge point, we list the set of all inputs (domain) and the set of all outputs (range):

• Domain: \(\{\text{Alice}, \text{Brad}, \text{Carl}\}\)
• Range: \(\{\text{cat}, \text{dog}\}\)

Match with the given options

We compare our findings with the choices:

• Option A states it is a function with domain \(\{\text{Alice}, \text{Brad}, \text{Carl}\}\) and range \(\{\text{cat}, \text{dog}\}\). This matches our analysis.

Answer:

• **A. function

domain: {Alice,Brad,Carl}
range: {cat,dog} (Correct answer)**

• B. function

domain: {cat,dog}
range: {Alice,Brad,Carl}

• C. not a function