CONTENT OUTLINE
Unit 1: Functions
Time Advisory: This unit should take you approximately 14.5 hours to complete.
 Subunit 1.1: 3.5 hours
 Subunit 1.2: 2 hours
 Subunit 1.3: 2 hours
 Subunit 1.4: 1.5 hours
 Subunit 1.5: 4 hours
 Subunit 1.6: 1.5 hours
Functions create a basic structure in mathematics. Some mathematicians describe
them as well-functioning machines in which you can choose an input and count on the
machine always producing the same output for that particular input. If a soda machine
functions properly, you can input money and press cola, and the outcome is a cola. It
won’t be root beer—you can count on it! A mathematical function is predictable in the
same way. For example, maybe a function gives an output of 3.47 when you input the
number -6. If it is truly a function, it will always give an output of 3.47 when you input the
number -6. This first unit focuses on defining functions, identifying specific notation that
we will be using, and helping you develop an understanding of certain characteristics of
functions and their graphs.
Learning Outcomes:
Upon successful completion of this unit, the student will be able to:
 Create examples of functions and nonfunctions.
 Describe attributes of relations that are not functions.
 Determine the attributes of domain and range of a given function.
 Determine whether a function is one-to-one.
 Demonstrate facility with function notation.
 Demonstrate facility with functions in words, tables, graphs, and formulas.
 Execute the horizontal and vertical line tests.
 Evaluate a function at a specific input value.
 Solve a function given a specific output value.
 Evaluate piecewise functions.
 Calculate rates of change.
 Describe basic behaviors of graphs of functions.
 Compose functions and determine the resultant domain and range of the new
function.
 Transform functions.
Standards Addressed (Common Core):
 CCSS.Mathematics.F-BF-1a, 1b, 1c, 3, 4a, 4b, 4c
 CCSS.Mathematics.F-IF-1, 2, 4, 5, 6, 7a, 7b, 7c, 7d, 7e
 CCSS.Mathematics.A-REI-10
 CCSS.Mathematics.F-LE-2
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CCSS.Mathematics.A-SSE-3
CCSS.Mathematics.A-APR-3
CCSS.Mathematics.A-CED-4
1.1
Functions and Function Notation
At a picnic, the number of sandwiches depends upon the number of picnickers. In a
theater, the number of dollars collected depends upon the number of tickets sold. The
cost of a taxi depends upon the number of miles driven. These are examples of
functions, which are relations that create a unique output for any particular input. This
subunit focuses on the definition of function both formally and informally.
The notation may be intimidating at first, but it makes later topics easier. Remember
that you already think in notation. The problem “Fifty-four minus thirty-nine” is easier to
solve when written in the notation: 54 – 39. Mathematics uses notation to simplify things
and make it easier to think; it just takes time for your brain to learn new notational
language.
Subunit 1.1 begins by defining functions and explaining a variety of ways to describe
them, such as notation, graphs, and charts. It continues by introducing a set of
important toolkit functions that will be extremely useful in subsequent parts of the
course.
Instruction: Lippman and Rasmussen’s Precalculus: An Investigation of Functions
Link: Lippman and Rasmussen’s Precalculus: An investigation of Functions.
Instructions: Please Read pages 1–2 of this text, focusing on “What is a Function.” As
you complete the reading, use pencil and paper to work through the examples and do
the “Try It Now” problems on page 2. (Answers are on page 12.)
Standards Addressed (Common Core):
 CCSS.Math.Content.HSF-IF.A.1
 CCSS.Math.Content.HSF-IF.A.2
 CCSS.Math.Content.HSF-IF.B.5
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