Functions, Domain, and Range

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

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 function to be negative?

Back

A function is negative when its output values (y-values) are less than zero.

Front

Identify the domain of the function g(x) = 1/(x-2).

Back

The domain is all real numbers except x = 2, since the function is undefined at that point.

Front

Identify the range of the function f(x) = x^2.

Back

The range is all real numbers y such that y >= 0, since the output of a square function is always non-negative.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve 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 every x-value, there is a unique y-value.

Front

What is a non-function?

Back

A non-function is a relation where at least one input is associated with multiple outputs. For example, the relation {(1,2), (1,3)} is not a function.