Questions: Relation 3 Domain Range x door z paper a door k leaf a pencil v leaf Relation 4 Domain Range -6 -6 -6 3 -6 9 6 -7 Function Not a function Function Not a function

Relation 3
Domain Range
x door
z paper
a door
k leaf
a pencil
v leaf

Relation 4
Domain Range
-6 -6
-6 3
-6 9
6 -7

Function
Not a function
Function
Not a function

Transcript text: Relation 3 \begin{tabular}{|c|c|} \hline Domain & Range \\ \hline$x$ & door \\ \hline$z$ & paper \\ \hline$a$ & door \\ \hline$k$ & leaf \\ \hline$a$ & pencil \\ \hline$v$ & leaf \\ \hline \end{tabular} Relation 4 \begin{tabular}{|c|c|} \hline Domain & Range \\ \hline-6 & -6 \\ \hline-6 & 3 \\ \hline-6 & 9 \\ \hline 6 & -7 \\ \hline \end{tabular} Function Not a function Function Not a function

Solution

Solution Steps

To determine if a relation is a function, we need to check if each element in the domain maps to exactly one element in the range. If any element in the domain maps to more than one element in the range, it is not a function.

For Relation 3:

Check if any domain value maps to more than one range value.

For Relation 4:

Check if any domain value maps to more than one range value.

Step 1: Define the Relations

We are given two relations:

Relation 3: $\{(x, \text{door}), (z, \text{paper}), (a, \text{door}), (k, \text{leaf}), (a, \text{pencil}), (v, \text{leaf})\}$
Relation 4: $\{(-6, -6), (-6, 3), (-6, 9), (6, -7)\}$

Step 2: Determine if Relation 3 is a Function

A relation is a function if each element in the domain maps to exactly one element in the range. In Relation 3, the domain element $a$ maps to both $\text{door}$ and $\text{pencil}$. Therefore, Relation 3 is not a function.

Step 3: Determine if Relation 4 is a Function

In Relation 4, the domain element $-6$ maps to $-6$, $3$, and $9$. Therefore, Relation 4 is not a function.