3.1 Functions Ex 1: Some real-life situations: Describe the set of inputs, the set of outputs, and the rule for the following functions: The amount of income tax you pay depends on your income Suppose a rock is dropped straight down from a high place. Physics tells us that the distance traveled by the rock in t seconds is 16t^2 feet.

Example 2: Evaluating a Function Example 3: Finding a difference Quotient

Example 4: Determining if an Equation Defines a Function A function can be defined by an equation of two variables: Example 4: Determining if an Equation Defines a Function

Domain of a Function Unless the information to the contrary is given, the domain of a function f consists of every real number input for which the function rule produces a real number output. Watch out for: Division by zero The square root (or nth root, where n is a even number) of a negative number

Applications and The Domain Convention A real-life situation may lead to a function whose domain does not include all the values for which the rule of the function is defined.

Piecewise-Defined Functions A piecewise-defined function is one whose rule includes several formulas. The formula for each piece of the function is applied to certain values of the domain, as specified in the definition of the function

Greatest Integer Functions For any number x, round down to the nearest integer less than or equal to x.

3.1 Hmwr:1-4, 5-41odd, 42, 43-61, 65, 67, 69, 71 (Hmwr given over two days)