5.1: Is This a Function? (Tables)

Front

What is a function?

Back

A function is a relation where each input (x) has exactly one output (y).

Front

What is a relation?

Back

A relation is a set of ordered pairs, which may or may not have a unique output for each input.

Front

True or False: A function can have multiple outputs for the same input.

Back

False.

Front

What does it mean for a relationship to be a function?

Back

It means that for every input (x), there is only one corresponding output (y).

Front

How can you determine if a table represents a function?

Back

Check if any input (x) value is repeated with different output (y) values.

Front

What is the vertical line test?

Back

A method to determine if a graph represents a function; if a vertical line crosses the graph more than once, it is not a function.

Front

Example of a function: (1, 2), (2, 3), (3, 4). Is this a function?

Back

Yes, each input has exactly one output.

Front

Example of a relation: (1, 2), (1, 3), (2, 4). Is this a function?

Back

No, the input '1' has two different outputs (2 and 3).

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point in a coordinate system.

Front

If a table has the pairs (2, 5), (3, 5), (4, 6), is it a function?

Back

Yes, each input has one output, even though the output '5' is repeated.