Domain and Range, Functions

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

What is the domain of a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output) that the function can produce.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a graph of a function. If a vertical line intersects the graph at more than one point, then it is not a function.

Front

What is the horizontal line test?

Back

The horizontal line test is used to determine if a function is one-to-one. If any horizontal line intersects the graph more than once, the function is not one-to-one.

Front

How do you find the domain of a function given a graph?

Back

To find the domain from a graph, identify all the x-values for which the graph has points. The domain is the set of these x-values.

Front

How do you find the range of a function given a graph?

Back

To find the range from a graph, identify all the y-values that the graph reaches. The range is the set of these y-values.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, typically written as (x, y).

Front

What does it mean for a set of ordered pairs to represent a function?

Back

A set of ordered pairs represents a function if no two different ordered pairs have the same first element (x-value).

Front

What is a one-to-one function?

Back

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