Identifying Functions

Front

What is a function?

Back

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

Front

How can you identify a function from a set of ordered pairs?

Back

A set of ordered pairs is a function if no x-value is repeated with different y-values.

Front

What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, the graph is not a function.

Front

Is the relation {(1,2), (2,3), (1,4)} a function?

Back

No, because the x-value 1 has two different y-values (2 and 4).

Front

Is the relation {(3,5), (4,5), (5,5)} a function?

Back

Yes, because each x-value has only one y-value.

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if every x-value corresponds to only one y-value.

Front

Which of the following is a function: {(2,3), (3,4), (2,5)} or {(1,2), (2,3), (3,4)}?

Back

{(1,2), (2,3), (3,4)} is a function because it has no repeated x-values.

Front

What is an example of a function in real life?

Back

An example of a function is a vending machine: each button (input) gives one specific snack (output).

Front

Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, as long as each x-value has only one y-value.

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, which can include functions.