Algebra 15 - Functions

The lecture introduces functions as a special type of binary relation, explaining how they map elements from a domain to a range, with each input having exactly one output. It covers the concepts of domain, range, and codomain, and provides examples using favorite fruits to illustrate valid and invalid functions. The lecture also discusses the graphical representation of functions as ordered pairs, often visualized on a Cartesian plane.

What distinguishes a function from a general binary relation?

• A function does not require a specific output for each input.

• A function relates each element of one set to exactly one element of another set.

• A function can relate one element to multiple elements.

• A function can have multiple inputs for a single output.

How is the output of a function typically represented?

• As f(x), where x is the input.

• As a division of inputs.

• As a product of inputs.

• As a sum of inputs.

What is the domain of a function?

• The set of all possible inputs.

• The set of all real numbers.

• The set of all imaginary numbers.

• The set of all possible outputs.

What is the codomain of a function?

• The set of all possible inputs.

• The set of all real numbers.

• The set of all possible outputs.

• The set containing the range.

In the context of functions, what is the range?

• The set of all real numbers.

• The subset of the codomain that includes all actual outputs.

• The set of all elements in the codomain.

• The set of all possible inputs.

How can functions be represented graphically?

• As a single point on a graph.

• As a set of ordered pairs on a Cartesian plane.

• As a line of text.

• As a list of numbers.

In algebra, what type of elements do the domain and range of functions typically contain?

• Complex numbers.

• Whole numbers.

• Imaginary numbers.

• Real numbers.