Question

1. ccss model with mathematics students were asked about the number of cell phone minutes they use. some of the responses are shown in the table. make a mapping diagram for the relation.

student | sarah | max | jacob | rebekah
number of minutes | 275 | 220 | 350 | 275
is this relation a function? explain.

1. ccss model with mathematics make a table and a mapping diagram for the relation {(0, −2), (1, −2), (1, 3), (1, 8)}.

domain | | | |
range | | | |
is this relation a function? explain.

Explanation:

Problem 1

Step1: Identify Domain and Range

Domain (students): Sarah, Max, Jacob, Rebekah
Range (minutes): 275, 220, 350 (note 275 repeats, but range is unique values or all outputs)

Step2: Mapping Diagram

Draw two ovals: left (domain) with students, right (range) with minutes. Draw arrows: Sarah→275, Max→220, Jacob→350, Rebekah→275.

Step3: Check if Function

A function has each domain element map to exactly one range element. Here, each student (domain) maps to one minute (range). Even though 275 is repeated (range), the domain elements are unique. So it is a function.

Step1: Identify Domain and Range from Ordered Pairs

Ordered pairs: \((0, -2)\), \((1, -2)\), \((1, 3)\), \((1, 8)\)
Domain (x - values): \(0, 1\) (unique x - values)
Range (y - values): \(-2, 3, 8\) (unique y - values, or all outputs: \(-2, -2, 3, 8\) → unique: \(-2, 3, 8\))

Step2: Make a Table

Domain (x)	0	1	1	1

Step3: Mapping Diagram

Left oval (domain): \(0, 1\); Right oval (range): \(-2, 3, 8\). Arrows: \(0→ - 2\), \(1→ - 2\), \(1→3\), \(1→8\).

Step4: Check if Function

A function requires each domain element to map to exactly one range element. Here, \(1\) (domain) maps to \(-2\), \(3\), and \(8\) (multiple range elements). Thus, it is not a function.

Answer:

• Mapping Diagram: Domain {Sarah, Max, Jacob, Rebekah}, Range {220, 275, 350}; arrows as above.
• Is it a function? Yes. Explanation: Each student (domain) is paired with exactly one number of minutes (range).

Problem 2