Function or Not Function

Front

What is a function?

Back

A function is a relation in which each input (x-value) is associated with exactly one output (y-value).

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, typically represented as (x, y).

Front

How can you determine if a set of ordered pairs is a function?

Back

A set of ordered pairs is a function if no two pairs have the same first element (x-value) with different second elements (y-values).

Front

Example of a function: {(-1, 2), (0, 3), (1, 4)}

Back

This is a function because each x-value is unique.

Front

Example of a non-function: {(1, 2), (1, 3), (2, 4)}

Back

This is not a function because the x-value '1' is associated with two different y-values (2 and 3).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What does it mean for a relation to be one-to-one?

Back

A one-to-one relation is a function where each output (y-value) is associated with exactly one input (x-value).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.