1. 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.

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

3. 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

4. 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

5. 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.

6. 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

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

8. 3.1 Hmwr:1-4, 5-41odd, 42, 43-61, 65, 67, 69, 71 (Hmwr given over two days)