PreCalculus

1. PreCalculus Chapter 1 Section 2 Functions and Their Properties

2. What is a Function? • A function is like a machine that excepts input values (x) and enacts a procedure on the input to produce an output (y). • We call the input values (x), the Domain of the function and we call the output values (y), the Range of the function. • See page 86 for the official definition of function, domain and range.

3. Function Notation • We use Leonhard Euler’s elegant function notation y = f(x) • Which reads as “y equals f of x” or “the value of f at x”. • Here we say that x is the independent variable and that y is the dependent variable.

4. Graphs of Functions • One of the best ways to “look” at functions is graphically. • The graph of the function y = f(x) is the set of all coordinate points (x, y) or (x, f(x)) • In fact we can use a vertical line test to determine if a graph is indeed a function based on the definition of a function. • A graph is a function if and only if no vertical line intersects more than one point.

5. Domain of a Function • The domain of a function is the set of all numbers (x) that allow the function to work. The x-values. • We start very simply with the idea that all of the real numbers (x) work. • Then we look at special details about the functions that might limit the values of x that don’t let the function work. • See Examples on page 88.

6. Range of a Function • The range of a function is the output values or y-values of a function. • Again, we start with the idea that all of the real numbers (y) work. • Then we look at special cases where some y-values can’t work. • This is best determined from the graph of the function. • See examples 3 and 4 on pages 88 – 89.

7. Homework Part 1 • Do Exercises # 1 – 19 page 102.