IS THIS A FUNCTION?

Front

What is a function in mathematics?

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 relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

Front

What is the vertical line test?

Back

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

Front

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

Back

A graph represents a function if for every x-coordinate, there is only one corresponding y-coordinate.

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 corresponds to 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 x^2.

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 y^2 = x, where a single x-value can correspond to two different y-values.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with its output.

Front

What is the definition of 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 can produce the same output.

Front

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

Back

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