3-1 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) 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

What is the domain of a relation?

Back

The domain is the set of all possible input values (x) for the relation.

Front

What is the range of a relation?

Back

The range is the set of all possible output values (y) for the relation.

Front

How do you determine if a relation is a function?

Back

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

Front

What is a linear function?

Back

A linear function is a function whose graph is a straight line, represented by the equation y = mx + b.

Front

What is a nonlinear function?

Back

A nonlinear function is a function whose graph is not a straight line, meaning it does not have a constant rate of change.

Front

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

Back

A one-to-one function is a function where each output (y) is associated with exactly one input (x), meaning no two different inputs produce the same output.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if any vertical line intersects the graph at more than one point, it is not a function.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where for each x, there is exactly one corresponding y.