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 no input is paired with more than one output.

Front

What does it mean if a table does not represent a function?

Back

If a table does not represent a function, it means that at least one input is associated with multiple outputs.

Front

What is the vertical line test?

Back

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

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.

Front

What is an example of a function?

Back

An example of a function is f(x) = x^2, where each input x has a unique output.

Front

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

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 is associated with two different outputs.

Front

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

Back

A graph represents a function if every x-coordinate (input) corresponds to exactly one y-coordinate (output).

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is paired with exactly one input, meaning no two different inputs have the same output.

Front

What is a many-to-one function?

Back

A many-to-one function is a function where multiple inputs can produce the same output.