A relation is a function if each input (or domain element) corresponds to exactly one output (or range element). In other words, no input can map to more than one output.

Given the relation $\{(1, 2), (1, 7), (7, 2), (7, 7)\}$:

• The input $1$ is paired with both $2$ and $7$.
• The input $7$ is paired with both $2$ and $7$.

Since the input $1$ maps to two different outputs (both $2$ and $7$), and the input $7$ also maps to two different outputs, this relation is not a function.

Domain:

The domain is the set of all inputs. So, the domain is: $\{1, 7\}$

Range:

The range is the set of all outputs. So, the range is: $\{2, 7\}$

Conclusion:

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

Would you like more details or have any questions?

Here are some related questions:

1. What conditions make a relation a function?
2. Can a function have repeated outputs for different inputs?
3. How would the relation change if we remove the pair $(1, 7)$?
4. How do we graphically represent a function and a non-function?
5. What is the vertical line test for determining if a relation is a function?

Tip: In a function, every input must have exactly one output.