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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 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 Second, feeling of the tuskCried, “Ho what have we here

So very round and smooth and sharp?To me ‘tis mighty clear

This wonder of an ElephantIs very like a spear!”

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 ElephantIs very like a snake!"

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!” The Fifth, who chanced to touch the ear,

Said: "E'en the blindest manCan tell what this resembles most;

Deny the fact who canThis marvel of an Elephant

Is very like a fan!"

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!"

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!

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

1

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. ____________________________________________________________________________________

2

Explain how you could accurately identify the parts of the function that are linear. ____________________________________________________________________________________

3. Let’s look at the individual pieces of the previous piecewise function. Identify each type of function and provide its equation.

a.

f(x) =

equation

function type

2018161412

10

8

6

4

2

108642

b.

f(x) =

equation

function type

2018161412

10

8

6

4

2

108642

c.

f(x) =

equation

function type

2018161412

10

8

6

4

2

108642

3

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. ____________________ 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.

4

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.

5

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. ____________________________________ ____________________________________________________________________________________________________________________________________________________________

6

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?







7

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.

8

Write and graph the piecewise function for large envelopes given below.

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 xMake a graph for the function

f(x) = xwhere the carrier charges 3¢/min.

Challenge: 2 = ? = ?2.1 = ?2.9 = ?2.9 = ?2.1 = ?

9

Culminating Task: Select any company’s logo and construct it in Geometer's Sketchpad as a piecewise function.

10

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