Functions and Non-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

What is a non-function?

Back

A non-function is a relation where at least one input is related to more than one output.

Front

How can you determine if a relation is a function?

Back

You can use the vertical line test: if a vertical line intersects the graph of the relation at more than one point, it is not a function.

Front

What is the domain of a function?

Back

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

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

Give an example of a function.

Back

An example of a function is f(x) = 2x + 3, where each input x has a unique output.

Front

Give an example of a non-function.

Back

An example of a non-function is the relation {(1, 2), (1, 3)}, where the input 1 is related to two different outputs.

Front

What does it mean for a function to be one-to-one?

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 mapping diagram?

Back

A mapping diagram visually represents the relationship between inputs and outputs of a function, showing how each input is paired with an output.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.