Relations and Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

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

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.

Front

What is the domain of a function?

Back

The domain is the set of all possible input values (x-values) for a function.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) that a function can produce.

Front

How can you determine if a graph represents a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What does the mapping {(0, 1), (1, 2), (2, 2), (3, 4)} represent?

Back

It represents a relation where each input (0, 1, 2, 3) is paired with an output (1, 2, 2, 4).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

What is an example of a non-function relation?

Back

An example is the relation {(1, 2), (1, 3)}, where the input 1 is associated with two different outputs.

Front

What is the significance of the range in a function?

Back

The range indicates all the possible outputs of a function, which helps in understanding the behavior of the function.