Educational worksheet on relations and functions, including definitions, examples, and exercises for understanding mathematical functions.

- Relations: A set of ordered pairs of inputs and outputs.
- Functions: A relation where each input has exactly one output.
- Vertical Line Test: A method to determine if a graph represents a function; if any vertical line intersects the graph more than once, it is not a function.
- Domain: The set of all possible input values (x-values) for a function.
- Range: The set of all possible output values (y-values) for a function.

For the table:
- x: 15, 3, 15, 15
- y: 3, 3, 15, 21
- Number of quantities arranged in columns and rows: 4
- Function: No (since x = 15 corresponds to multiple y-values: 3, 15, 21)
- Domain: {15, 3}
- Range: {3, 15, 21}

For the graph:
- A pictorial representation of data.
- Function: No (fails vertical line test)
- Domain: (-∞, ∞)
- Range: [0, ∞)

For the mapping:
- Pairing each member of the domain with each member of the range.
- Domain: {1, 2, 3, 4}
- Range: {2, 4, 6, 8}
- Function: No (since 2 maps to both 4 and 6)
- Domain: {1, 2, 3, 4}
- Range: {2, 4, 6, 8}

For the ordered pair of inputs and outputs in a set:
- {(−7, 2), (−3, 4), (1, 5), (−7, 6), (8, 9)}
- Function: No (since −7 maps to both 2 and 6)
- Domain: {−7, −3, 1, 8}
- Range: {2, 4, 5, 6, 9}