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 mapping is a function?

Back

A mapping 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 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 does it mean for a relation to not be a function?

Back

A relation is not a function if at least one x-value is associated with multiple y-values.

Front

How can you represent a function using ordered pairs?

Back

A function can be represented as a set of ordered pairs (x, y) where each x-value is unique.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique corresponding y-value.

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 {(1, 2), (1, 3)}, where the x-value 1 is paired with two different y-values.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each y-value is paired with exactly one x-value, meaning no two different x-values map to the same y-value.