Functions and Relations

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Front

How can you determine if a relation is a function?

Back

A relation is a function if no x-value is paired with more than one y-value.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) for the function.

Front

What does it mean for a set of ordered pairs to represent a function?

Back

It means that each x-value in the set is associated with exactly one y-value.

Front

What is an example of a non-function relation?

Back

The relation {(1,2), (1,3)} is not a function because the x-value 1 is paired with two different y-values.

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 curve at more than one point, it is not a function.

Front

What are ordered pairs?

Back

Ordered pairs are pairs of numbers (x, y) that represent coordinates in a Cartesian plane.

Front

What is the significance of the x-value in a function?

Back

The x-value is the input of the function, which determines the corresponding y-value (output).

Front

What is a mapping in the context of functions?

Back

A mapping is a way to describe how each element of the domain is paired with an element in the range.