 One quantity depends on another quantity  # of shirts -> revenue  Age -> Height  Time of day -> Temperature 3.1 Function

Function-Definition 4 Representations of a function: Verbally – Numerically – Algebraically – Visually – Formal definition: A function f is a rule that assigns to each element x in a set A exactly one element, f(x), in a set B. ( f(x) is read as “ f of x ”)

Verbal & Numeric Verbal: Function f(x) divides x by 3 and then adds 4. A B Numeric: x f(x) Table describes the values in A and their assignments in B.

Algebraic & Graphic Algebraic: Graphic: x f(x) Plot points (x, f(x)) in the two dimensional plane x f(x)

Example: Evaluate the function at the indicated values.

Piecewise Functions Evaluate the function at the indicated values.

Difference Quotient Find f(a), f(a+h), and the difference quotient for the given function. Difference quotient:

Domain Domain: the set of all inputs for which the function is a real number. (valid x) Recall definition: A function f is a rule that assigns to each element x in a set A exactly one element, f(x), in a set B. Set A = input => x = independent variable Set B = output => y = f(x) = dependent variable Two restrictions on the domain for any function :

Example 1 Find the domain for the following function. D:

Example 2 Find the domain for the following function. D: