Function vs. Relation

Front

What is a relation in mathematics?

Back

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

Front

What is a function?

Back

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

Front

How can you determine if a relation is a function?

Back

You can determine if a relation is a function by checking if any input (x) is paired with more than one output (y). If it is, then it is not a function.

Front

What is the vertical line test?

Back

The vertical line test is a method used 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

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 is associated with two different outputs.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x) 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) that the function can produce.

Front

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

Back

A function is one-to-one if each output (y) is associated with exactly one input (x). No two different inputs can produce the same output.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with its corresponding output.