Relations and Functions / Linear 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 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

What does it mean for a relation to be a function?

Back

For a relation to be a function, each x-value must correspond to only one y-value.

Front

Give an example of a function.

Back

An example of a function is the relation {(1, 2), (2, 3), (3, 4)}.

Front

Give an example of a relation that is not a function.

Back

An example of a relation that is not a function is the relation {(1, 2), (1, 3)}.

Front

What is the domain of a function?

Back

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

Front

What does it mean for a graph to pass the vertical line test?

Back

If a graph passes the vertical line test, it means that for every x-value, there is only one corresponding y-value, confirming it is a function.

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph, typically in the form y = mx + b.