Lecture Notes Waner and Constenoble Section 1.1
Section 1.1 Functions from the Numerical, Algebraic, and Graphical Viewpoints
 Use Interval Notation, inequalities and graphs to describe subsets of the real line.
 Use tables, graphs and formulas to determine values of a given function on its domain.
 Practice using the notation that you will use to enter formulas into a spreadsheet,
including correct order of operations.
Example 1 page 44 iPod Sales
The total number of iPods sold by Apple up to the end of year x can be approximated by f (x)
million iPods, where
f (x) = 4x2 + 16x + 2
0≤x≤6
and x = 0 corresponds to 2003.
a. Domain
For what inputs is the formula 4x2 + 16x + 2 defined? __________________________________
What is the domain of f (x)? ______________________________________________________
For what dates does this formula model the total number of iPods sold? ____________________
______________________________________________________________________________
b. Interval notation
Express the inequalities in interval notation and as a graph on the number line.
i.
0≤x≤6
ii.
0<x≤6
iii.
x<6
iv.
0≤x
c. Evaluate and interpret
What is f (3)? Interpret your answer in the context of iPods.
f (3) = ________________ says that at the end of the year _________________, the total number
of iPods sold was approximately _________________________________ million iPods, which
is the same as _____________________________ iPods.
What is f (3.5)? Interpret your answer.
f (3.5) = ______________ says that on the date (month, day and year) _____________________,
the total number of iPods sold was approximately ________________________ million iPods,
which is the same as ____________________ iPods.
What is f (7)?
Lecture Notes Waner and Constenoble Section 1.1
d. Technology formulas
You will use a spreadsheet to analyze data.
 Typing formulas into a spreadsheet is similar to typing them into your calculator.
 The spreadsheet interprets parentheses and operators, like +, –, *, /, and ^, according to
the rules for order of operations.
 In a spreadsheet, always type * when you wish to multiply.
o For example, type 3*5, not 3(5) to multiply 3 and 5.
o Similarly, type 3*x, not 3x to multiply 3 and x.
WebAssign 1.1 includes problems in which you write “Technology formulas” for given
expressions. A "Technology Formula" is a formula that you would use on a spreadsheet.
Example
a. Write the technology formula for 4x2 + 16x + 2.
b. Write the technology formula for
4x  3
3x  1
c. Which of the following represent(s) a technology formula for 3x1/2?
3x^(1/2)
3(x)^(1/2)
(3*x)^(1/2)
3*x^1/2
3*(x)^1/2
3*x^(1/2)
(((3))*((x)^(1/2)))
Resources:
 At the end of each chapter, there is a “Technology Guide” for both graphing calculators
and spreadsheets.
 In the margins next to some examples, a “using Technology” note explains how to use
technology in given examples.