The given relation is:

$\{(3,1), (3,2), (7,1), (7,2)\}$

Determine if it's a function:

A relation is a function if every input (first component of the ordered pair) maps to exactly one output (second component).

In this case:

• For $x = 3$, there are two outputs: $1$ and $2$.
• For $x = 7$, there are also two outputs: $1$ and $2$.

Since an input maps to more than one output, this is not a function.

Domain:

The domain consists of the set of all inputs (first components) from the relation: $\{3, 7\}$

Range:

The range consists of the set of all outputs (second components) from the relation: $\{1, 2\}$

Final Answer:

• Is this a function? No.
• Domain: {3, 7}.
• Range: {1, 2}.

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. What defines a function in terms of relations?
2. Can a function have repeating outputs for different inputs?
3. What happens if every input has exactly one output, but multiple inputs share the same output?
4. How do we represent the domain and range of a function graphically?
5. If a relation only has distinct inputs with no repeated outputs, can it still fail to be a function?

Tip: In ordered pairs, focus on the first component to determine if it's a function. Each unique input must pair with exactly one output.