Question

1. demarco raises chickens. he tracks the number of eggs his chickens lay at the end of each week.

a. make an arrow diagram that represents the relation.
b. is this relation a function? explain.
(chart: week 1, eggs 7; week 2, eggs 13; week 3, eggs 13; week 4, eggs 22; week 5, eggs 26; week 6, eggs 22)

Explanation:

Part a: Arrow Diagram (Relations)

To create an arrow diagram for the relation between weeks (input) and eggs (output), we list the weeks (1, 2, 3, 4, 5, 6) and their corresponding eggs (7, 13, 13, 22, 26, 22). We draw arrows from each week to its egg count:

• Week 1 → 7
• Week 2 → 13
• Week 3 → 13
• Week 4 → 22
• Week 5 → 26
• Week 6 → 22

Part b: Is it a Function?

A function is a relation where every input (week) has exactly one output (egg count). Let’s check:

• Week 1: 1 output (7)
• Week 2: 1 output (13)
• Week 3: 1 output (13)
• Week 4: 1 output (22)
• Week 5: 1 output (26)
• Week 6: 1 output (22)

Even though some outputs (e.g., 13, 22) repeat for different inputs, the key is that each input has only one output. This satisfies the definition of a function.

Final Answers

a. Arrow diagram: Draw arrows from Week 1→7, 2→13, 3→13, 4→22, 5→26, 6→22.
b. Yes, this relation is a function because each week (input) maps to exactly one number of eggs (output).

Answer:

Part a: Arrow Diagram (Relations)

To create an arrow diagram for the relation between weeks (input) and eggs (output), we list the weeks (1, 2, 3, 4, 5, 6) and their corresponding eggs (7, 13, 13, 22, 26, 22). We draw arrows from each week to its egg count:

• Week 1 → 7
• Week 2 → 13
• Week 3 → 13
• Week 4 → 22
• Week 5 → 26
• Week 6 → 22

Part b: Is it a Function?

A function is a relation where every input (week) has exactly one output (egg count). Let’s check:

• Week 1: 1 output (7)
• Week 2: 1 output (13)
• Week 3: 1 output (13)
• Week 4: 1 output (22)
• Week 5: 1 output (26)
• Week 6: 1 output (22)

Even though some outputs (e.g., 13, 22) repeat for different inputs, the key is that each input has only one output. This satisfies the definition of a function.

Final Answers

a. Arrow diagram: Draw arrows from Week 1→7, 2→13, 3→13, 4→22, 5→26, 6→22.
b. Yes, this relation is a function because each week (input) maps to exactly one number of eggs (output).