Identifying functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input.

Front

How can you determine if a mapping diagram represents a function?

Back

A mapping diagram represents a function if each input is connected to exactly one output.

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 graph to be a function?

Back

A graph is a function if every x-value (input) has a unique y-value (output).

Front

What is an example of a relation that is not a function?

Back

A relation where an input corresponds to multiple outputs, such as the relation {(1, 2), (1, 3)}.

Front

What is the definition of a one-to-one function?

Back

A one-to-one function is a function where each output is associated with exactly one input.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has exactly one output, while a relation can have multiple outputs for a single input.

Front

What is a domain in the context of functions?

Back

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

Front

What is a range in the context of functions?

Back

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

Front

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

Back

A set of ordered pairs represents a function if no two pairs have the same first element (input) with different second elements (outputs).