Functions Graphs

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 graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is the Vertical Line Test?

Back

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

Front

What does it mean for a graph to be 'not a function'?

Back

A graph is 'not a function' if there exists at least one input that corresponds to multiple outputs.

Front

Can a function have more than one output for a single input?

Back

No, a function cannot have more than one output for a single input; this would violate the definition of a function.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is related to exactly one input, meaning no two different inputs produce 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.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or rules for different parts of its domain.