Relation vs. Function

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is the vertical line test?

Back

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

Front

What is the horizontal line test?

Back

The horizontal line test is used to determine if a function is one-to-one. If a horizontal line intersects the graph at more than one point, the function is not one-to-one.

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

Give an example of a function.

Back

An example of a function is the equation y = 2x + 3, where each x-value corresponds to one 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 set of points {(1, 2), (1, 3)}, where the input 1 has two different outputs.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point in a coordinate system.

Front

What is a mapping?

Back

A mapping is a way to describe how each element in one set (domain) is paired with an element in another set (range).

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 the function.

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 result from the function.