Relations and Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

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 (Vertical Line Test).

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 be a function?

Back

For a relation to be a function, each input must be associated with exactly one output.

Front

What is an ordered pair?

Back

An ordered pair is a pair of elements (x, y) where the first element is the input and the second element is the output.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output, while a relation can have multiple outputs for a single input.

Front

How do you find the domain from a graph?

Back

To find the domain from a graph, identify all the x-values that the graph covers.

Front

What is the significance of the vertical line test?

Back

The vertical line test is used to determine if a graph represents a function; if a vertical line intersects the graph more than once, it is not a function.