3.1 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

How can you determine if a set of ordered pairs is a function?

Back

A set of ordered pairs is a function if no two different ordered pairs have the same first element (input).

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 does it mean for a graph to be a function?

Back

A graph represents a function if every x-value (input) has exactly one corresponding y-value (output).

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each input x gives a unique output.

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)}, because the input 1 is related to two different outputs.

Front

What is a domain in 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 a range in 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 one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements; each output is unique.

Front

What is a linear function?

Back

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