Relation vs. Function

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 every input has exactly one output.

Front

How can you determine if a mapping is a function?

Back

A mapping is a function if no two ordered pairs have the same first element (x-value) with different second elements (y-values).

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 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

Give an example of a function.

Back

An example of a function is f(x) = 2x + 3, where each input x has a unique output.

Front

Give 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 does it mean for a function to be one-to-one?

Back

A function is one-to-one if each output is produced by exactly one input, meaning no two different inputs map to the same output.

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.