Question

each table represents a relation. represent the relation as a mapping diagram. then determine if the relation is a function.
21)

x	y
-4	0
-3	7
-2	6
0	-7
1	7
2	7
6	-7
7	7

22)

x	y
-5	5
-5	-3
-3	-7
-3	7
-3	3
-1	-7
-1	4
5	1

Explanation:

Step1: Identify domain and range (21)

Domain (x-values): $\{-4, -3, -2, 0, 1, 2, 6, 7\}$
Range (y-values): $\{-7, 0, 6, 7\}$

Step2: Check function rule (21)

Each x maps to exactly one y. No repeated x-values with different y-values.

Step3: Identify domain and range (22)

Domain (x-values): $\{-5, -3, -1, 5\}$
Range (y-values): $\{-7, -3, 1, 3, 4, 5, 7\}$

Step4: Check function rule (22)

x-values $-5, -3, -1$ map to multiple y-values.

Answer:

1. For relation 21:

Mapping diagram: Draw two columns. Left column (domain): $\boldsymbol{-4, -3, -2, 0, 1, 2, 6, 7}$. Right column (range): $\boldsymbol{-7, 0, 6, 7}$. Draw arrows:
$-4 \to 0$, $-3 \to 7$, $-2 \to 6$, $0 \to -7$, $1 \to 7$, $2 \to 7$, $6 \to -7$, $7 \to 7$.
This relation is a function.

1. For relation 22:

Mapping diagram: Draw two columns. Left column (domain): $\boldsymbol{-5, -3, -1, 5}$. Right column (range): $\boldsymbol{-7, -3, 1, 3, 4, 5, 7}$. Draw arrows:
$-5 \to 5$, $-5 \to -3$; $-3 \to -7$, $-3 \to 7$, $-3 \to 3$; $-1 \to -7$, $-1 \to 4$; $5 \to 1$.
This relation is not a function.