2.  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.  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.  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.  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.  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.  Do Exercises # 1 – 19 page 102.