What's the big deal about functions?

Informally: a relationship between two or more quantities ("variables").

Formally: One quantity (the dependent variable) is uniquely determined given the quantities (the independent variables) of which it is a function.

For example, your grade in this class is determined by your grades on the final, the hour exams, the quizzes, and the homework. We might write

G(F,E,Q,H)

or

G=g(F,E,Q,H)

to indicate that your grade G is a function of these four "sub-grades". This is called a multivariate function, since G is a function of multiple (more than one) variables (F, E, Q, and H).

In this class we'll more frequently encounter functions of a single variable (univariate functions). Are the following statements true in a formal or informal sense?

• "Student happiness is a function of student grades."
• "The state of the economy is a function of the Gross Domestic Product."
• "The area of a square is a function of the side length."