Relations and Functions

Front

What is the definition of a function?

Back

A function is a relation in which each input (or domain value) is associated with exactly one output (or range value).

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.

Front

How can you determine if a relation is a function using the vertical line test?

Back

If a vertical line intersects the graph of the relation at more than one point, then the relation is not a function.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value corresponds to one unique y-value.

Front

What is 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 corresponds to two different outputs.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b.

Front

What is the significance of the slope in a linear function?

Back

The slope of a linear function indicates the rate of change of the function; it represents how much y changes for a unit change in x.

Front

What is the difference between discrete and continuous functions?

Back

Discrete functions have distinct, separate values (like points), while continuous functions have an unbroken line or curve.

Front

What is a one-to-one function?

Back

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