Functions (general)

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a relation is a function. If a vertical line intersects the graph of the relation at more than one point, then it 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 (x-value) is associated with more than one output (y-value).

Front

Give an example of a function.

Back

An example of a function is the relation {(1, 2), (2, 3), (3, 4)}. Each x-value has a unique y-value.

Front

Give 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), (2, 4)}. The x-value '1' is associated with 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 an output.

Front

What is the definition of a domain in 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 definition of a range in 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 does it mean for a set of points to represent a function?

Back

A set of points represents a function if no x-value is repeated with a different y-value.

Front

What is the significance of the number of elements in the domain and range?

Back

In a function, the number of elements in the domain can be equal to or greater than the number of elements in the range, but not the other way around.