Function, Relations, Domain,and Range

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 in the domain, there is one and only one y-value in the range.

Front

What is a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y). Relations can be functions, but not all relations are functions.

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

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once. This is known as the vertical line test.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where for each x-value, there is a unique 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 the set of points {(1, 2), (1, 3)}, where the input 1 corresponds to two different outputs.

Front

What does it mean for a function to be linear?

Back

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

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each element of the domain is paired with an element of the range.

Front

What is the difference between discrete and continuous functions?

Back

Discrete functions have distinct, separate values (like points on a graph), while continuous functions have values that form an unbroken line or curve.