Question

a. for the following relation, the input, x is the age of boys and the output, y, is their corresponding heights, in inches. (7, 41), (8, 45), (9, 49), (10, 52), (10, 53), (11, 55), (12, 59)
b. fill the values in the table

x	y
8	45
9	49
10	52
10	53
11	55
12	59

c. plot the points. graph with age (yr) on x - axis and height (in.) on y - axis
d. complete the mapping diagram
age (yr) : 7, 8, 9, 10, 11, 12
height (in.) : 41, 45, 49, 52, 53, 55, 59
e. state the domain of the relation
{7, , , , , __}
f. state the range of the relation
{41, , , , , , }
express the relation as a table, as a graph, and as a mapping diagram.

1. {(5, 3), (4, 3), (3, 3), (2, 3), (1, 3)}

table, graph, and mapping diagram templates for the relation {(5, 3), (4, 3), (3, 3), (2, 3), (1, 3)}

Explanation:

Part 1: Table Representation

Step1: Identify x and y values

The relation is \(\{(5, 3), (4, 3), (3, 3), (2, 3), (1, 3)\}\). So \(x\)-values are 5, 4, 3, 2, 1 and \(y\)-value is 3 for all.

Step2: Fill the table

\(x\)	\(y\)
4	3
3	3
2	3
1	3

Part 2: Graph Representation

Step1: Identify coordinates

The points are \((5, 3)\), \((4, 3)\), \((3, 3)\), \((2, 3)\), \((1, 3)\).

Step2: Plot points

On a coordinate plane, plot each point. The \(x\)-axis will have values 1 - 5 and \(y\)-axis value 3. All points lie on the horizontal line \(y = 3\) at \(x = 1, 2, 3, 4, 5\).

Part 3: Mapping Diagram

Step1: Identify domains and range

Domain (input) values: 1, 2, 3, 4, 5. Range (output) value: 3.

Step2: Draw mapping

Draw two ovals. Left oval (domain) has 1, 2, 3, 4, 5. Right oval (range) has 3. Draw arrows from each domain value to 3.

Final Output for Table:

\(x\)	\(y\)
4	3
3	3
2	3
1	3

Final Output for Graph:

Plot the points \((1, 3)\), \((2, 3)\), \((3, 3)\), \((4, 3)\), \((5, 3)\) on a coordinate plane (all on the horizontal line \(y = 3\)).

Final Output for Mapping Diagram:

• Domain (left oval): 1, 2, 3, 4, 5
• Range (right oval): 3
• Arrows: From 1, 2, 3, 4, 5 to 3.

Answer:

Step1: Identify domains and range

Domain (input) values: 1, 2, 3, 4, 5. Range (output) value: 3.

Step2: Draw mapping

Draw two ovals. Left oval (domain) has 1, 2, 3, 4, 5. Right oval (range) has 3. Draw arrows from each domain value to 3.

Final Output for Table:

\(x\)	\(y\)
4	3
3	3
2	3
1	3

Final Output for Graph:

Plot the points \((1, 3)\), \((2, 3)\), \((3, 3)\), \((4, 3)\), \((5, 3)\) on a coordinate plane (all on the horizontal line \(y = 3\)).

Final Output for Mapping Diagram:

• Domain (left oval): 1, 2, 3, 4, 5
• Range (right oval): 3
• Arrows: From 1, 2, 3, 4, 5 to 3.