We need only to experience a small part of something before making a judgment about the whole thing. When we
do this we are sometimes in error. The Blind Men and the Elephant illustrates this point.
The Parable of the Blind Men and the Elephant
It was six men of Indostan
To learning much inclined,
Who went to see the Elephant
(Though all of them were blind),
That each by observation
Might satisfy his mind
The Fifth, who chanced to touch the ear,
Said: "E'en the blindest man
Can tell what this resembles most;
Deny the fact who can
This marvel of an Elephant
Is very like a fan!"
The First approached the Elephant,
And happening to fall
Against his broad and sturdy side,
At once began to bawl:
"God bless me! but the Elephant
Is very like a wall!"
The Sixth no sooner had begun
About the beast to grope,
Than, seizing on the swinging tail
That fell within his scope,
"I see," quoth he, "the Elephant
Is very like a rope!"
The Second, feeling of the tusk
Cried, “Ho what have we here
So very round and smooth and sharp?
To me ‘tis mighty clear
This wonder of an Elephant
Is very like a spear!”
And so these men of Indostan
Disputed loud and long,
Each in his own opinion
Exceeding stiff and strong,
Though each was partly in the right,
And all were in the wrong!
The Third approached the animal,
And happening to take
The squirming trunk within his hands,
Thus boldly up and spake:
"I see," quoth he, "the Elephant
Is very like a snake!"
Moral:
So oft in theologic wars,
The disputants, I ween,
Rail on in utter ignorance
Of what each other mean,
And prate about an Elephant
Not one of them has actually seen
The Fourth reached out an eager hand,
And felt about the knee.
What most this wondrous beast is like
Is mighty plain," quoth he;
“Tis clear enough the Elephant
Is very like a tree!”
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Part 1
Unit 9: Piecewise Functions
.
While mathematics and life's lessons seem unrelated at times, they have much in common.
Because of their similarities, math is a great vehicle for understanding the world around us.
In the preceeding parable, six men falsely constructed a complete picture of an elephant based only on
the part of the animal they observed. While analyzing mathematical functions, the same temptation
exists.
1. Look for patterns in the function below. Would it be possible to mistakenly judge the nature of this
function if you based your analysis on just one part? _________ Explain. ______________________
____________________________________________________________________________________
_____________________________________________________________________________________
2. Let’s assume that someone described the function above as linear. Explain how is their statement is
partially correct.
____________________________________________________________________________________
Explain how that same statement is also false.
____________________________________________________________________________________
Explain how you could accurately identify the parts of the function that are linear.
____________________________________________________________________________________
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3. Let’s look at the individual pieces of the previous piecewise function.
Identify each type of function and provide its equation.
a.
10
8
function type
6
4
f(x) =
2
2
b.
4
6
8
10
12
14
16
18
equation
20
10
8
function type
6
4
f(x) =
2
2
c.
4
6
8
10
12
14
16
18
equation
20
10
8
function type
6
4
f(x) =
2
2
4
6
8
10
12
14
16
18
20
equation
4. Only a piece of each of the functions above was used to form the piecewise function in
question 1. Using numbers and symbols, identify the piece of each function that is used.
a. ____________________
b. ____________________
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c. ____________________
Piecewise functions are functions that cannot be represented by just one equation. Each equation
corresponds to a different part of the domain in the same way that in the parable each man’s idea
of an elephant corresponded to the part of the elephant he had experienced.
Let’s practice with more piecewise functions.
5. Write the piecewise function for the figure at right. You should identify the domain that
corresponds with each equation.
f(x) =
6. Write the piecewise function for the figure below.
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Part 2
Wholesale Pricing
Piecewise functions have many applications in real-world contexts. One such example is in the
business conducted between retail purchasers and wholesale distributors. In the following
advertisement, a distributor sells glow bracelets at different prices depending on the size of the
order. Explain why a distributor might be willing to sell product at a lower price if it is
purchased in bulk quantities. ____________________________________________________
______________________________________________________________________________
_______________________________
8. Use the prices listed in the advertisement above to graph the relationship between the quantity
of bracelets sold (per tube) and the purchasing price (up to 15 tubes) on the grid below.
9. Write the piecewise function for this graph.
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Let’s look at another example from the same wholesale company.
10. Once again, graph the relationship between the quantity of bracelets sold (per tube) and the
purchasing price (up to 55 tubes) on the grid below.
11. Write the piecewise function for this graph.
Summary of Parts 1 & 2
12. In The Parable of the Blind Man and the Elephant, the author said,
"Each in his own opinion
Exceeding stiff and strong,
Though each was partly in the right
And all were in the wrong."
Explain what the author means by this statement and then give a different example or relate a
personal experience that illustrates this same point. ____________________________________
______________________________________________________________________________
______________________________________________________________________________
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Day 2
15th Annual Kids First Scholarship Bedding Plant Sale
This annual sale is a fund raiser for the Kids First Scholarship Fund for tuition
assistance of the First United Methodist Church. Thank you for your support of this
mission that makes such a difference in children's lives. Preschool Advisory Council
Name ____________________________________________ Phone __________________________
Alternate Phone or Person To Contact about Order________________________________________
Email Address (for reminders/question about order)_______________________________________
How many bedding plants could you buy with $1.00?
How many bedding plants could you buy with $1.50?
How many bedding plants could you buy with $2.00?
How many bedding plants could you buy with $5.00?
How many bedding plants could you buy with $10.00?
How many bedding plants could you buy with $20.00?
How many bedding plants could you buy with $100.00?
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Challenge:
[[2]] = ?
[[]] = ?
[[2.1]] = ?
[[2.9]] = ?
[[-2.9]] = ?
[[-2.1]] = ?
The U.S. Postal Service uses such a system for their services. This has given rise to
the nickname "Postage Stamp Function". Graph and write this function for the
information provided below.
Write and graph the piecewise function for large envelopes given below.
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Cell phone carriers charge for their services by the minute or any portion thereof.
That means that for billing purposes they automatically round up to the next
minute. This is called a ceiling function and is represented by the notation
xMake a graph for the function
f(x) = x
where the carrier charges 3¢/min.
Challenge:
2 = ?
 = ?
2.1 = ?
2.9 = ?
2.9 = ?
2.1 = ?
Culminating Task: Select any company’s logo and construct it in Geometer's
Sketchpad as a piecewise function.
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