Is it 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

What is the definition of a mapping?

Back

A mapping is a relationship that pairs each element of one set with an element of another set.

Front

How can you determine if a relation is a function?

Back

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

Front

What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, then the relation is not a function.

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one input is associated with more than one output.

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.

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 the relation {(1, 2), (1, 3)}, where the input 1 is associated with two different outputs.

Front

What is 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 a many-to-one function?

Back

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