Functions from the Numerical, Algebraic, and Geometric Viewpoints
Let us start by looking at the definition in the textbook (and also in the topic summary)
f specified above by (Click on the correct graph.)Suppose that the function f is specified algebraically by the formula
The domain restriction means that we require in order for f(x) to be defined (the bracket indicates that included in the domain, and the bracket after the bracket indicates that included).
Now evaluate the given expressions. Fractions, decimals accurate to three decimal places, or valid technology formulas are permitted. Type if the function is not defined at the given value of x.
Piecewise Defined Functions
Sometimes we need more than a single formula to specify a function algebraically, as in the following example, similar to Example 2 in the textbook:
The number, in millions, of Facebook members from 2004 to 2009 can be approximated by the following function (t = 0 represents the start of 2004):^{†}
^{†}Sources for data: http://www.facebook.com and http://insidehighered.com

Facebook Members (Millions)

 We use the first formula : (see the green portion of the graph) to calculate n(t) if 0 ≤ t ≤ 3, or, equivalently, t is in [0, 3].
 We use the second formula: (see the orange portion of the graph) to calculate n(t) if 3 < t ≤ 5, or, equivalently, t is in (3, 5].
We use the first formula since 0 ≤ 2.5 ≤ 3.  
We use the second formula since 3 < 3.5 ≤ 5.  
n(5.5) is undefined.  The domain of n is [0, 5]. 
For the following questions, type if the function is not defined at the associated value of t. Here is the function again:
n(t) =  if 0 ≤ t ≤ 3  
if 3 < t ≤ 5 
Here is another piecewise defined function; this time with three formulas (notice that its graph now consists of three pieces):


You now have several options:
 Try some of the questions in the true/false quiz (warning: it covers the whole of Chapter 1) by going to the "Everything" page
 Try some of the questions in the chapter review exercises (Note: they cover the whole of Chapter 1.)
 Try some of the exercises in Section 1.1 of or .
Copyright © 2009 Stefan Waner