Identifying Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

How can you determine if a mapping represents a function?

Back

A mapping represents a function if every input (x-value) is paired with exactly one output (y-value).

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

Does the mapping {(1,2), (2,3), (3,4)} represent a function?

Back

Yes, because each input has exactly one output.

Front

Does the mapping {(1,2), (1,3), (2,4)} represent a function?

Back

No, because the input '1' is paired with two different outputs (2 and 3).

Front

Does the graph of a circle represent a function?

Back

No, because a vertical line can intersect the circle at two points.

Front

Does the graph of a straight line represent a function?

Back

Yes, as long as the line is not vertical.

Front

What is an example of a function in real life?

Back

A vending machine is a function; you select an item (input) and receive that item (output).

Front

What is a domain in a function?

Back

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

Front

What is a range in a function?

Back

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