Relations and Functions

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x-value) and an output (y-value).

Front

What is a function?

Back

A function is a special type of relation where each input (x-value) is associated with exactly one output (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

How do you determine the range from a graph?

Back

To determine the range from a graph, identify the lowest and highest points on the y-axis that the graph reaches.

Front

What is the difference between a relation and a function?

Back

A relation can have multiple outputs for a single input, while a function must have only one output for each input.

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.

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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 input 1 has two different outputs.

Front

What notation is used to represent the range of a function?

Back

The range is often represented using interval notation, such as [a, b] or (a, b).

Front

What does the notation (a, b) mean in interval notation?

Back

The notation (a, b) means that the interval includes all numbers between a and b, but does not include a and b themselves.