5.01 Getting Started(Functions—The Basics)

Chapter 5

Exponents and Functions

Chapter Introduction

• Read the introduction to the chapter on page 361, and then read the learning objectives for Investigation 5A. Don’t advance to the next slide until you’re done reading.

• By the end of lesson 5.06, you should meet the objectives listed.

• Today you will learn lessons 5.01 and 5.02.

For You to Explore

“Guess My Rule” game

Rule Breaker: the person who gives an input number to the Rule Maker. The Rule Breaker tries to figure out the rule based on responses by the Rule Maker (s/he tries to “break” the code, or rule.)

Rule Maker: the person who knows the rule (but keeps it secret) and gives the response, or output, for each input the Rule Breaker gives.

Example of playing “Guess My Rule”

The Rule Breaker says, “My input is 0.”

The Rule Maker says, “0 produces 0.”

The Rule Breaker says, “My input is 1.”

The Rule Maker says, “1 produces 3.”

The Rule Breaker says, “My input is 2.”

The Rule Maker says, “2 produces 6.”

The Rule Breaker says, “My input is 3.”

The Rule Maker says, “3 produces 9.”

Can you guess the rule?

Each input is multiplied by 3, or x produces 3x.

Input Output

0 0

1 3

2 6

3 9

For You to Explore

The rule that Sasha is using gives two different output numbers when using the same input value. The Rule Breaker cannot determine the rule when this happens. The rule must be predictable.

Turn to page 363 and answer the questions in problems 3-5.

For You to ExploreTurn to page 363 and answer the questions in problems 3-5.

a. If the rule is fair, c = 7 so that the input 2 has the same output each time.

b. a = b since they both represent the output when the input is 1.

c. We don’t have enough information since we don’t know the rule.

For You to ExploreTurn to page 363 and answer the questions in problems 3-5.

a. We cannot know Sasha’s responses since we don’t know if the coin landed on a head or tail.

b. Tony should complain about the rule since Sasha could give a different response to the same inputs depending on which side the coin lands on.

One More “Guess My Rule” Game

3 is added to each input, or “x returns x + 3.”

5.02 Building Functions

Chapter 5

Exponents and Functions

Minds in ActionTurn to pages 366-367 and read the discussion sections between Sasha and Tony, and then complete the table for the cost of purchasing a CD from the web site they refer to.

Don’t advance to the next slide until you’ve completed this.

Minds in ActionTurn to pages 366-367 and read the discussion sections between Sasha and Tony, and then complete the table for the cost of purchasing a CD from the web site they refer to.

Minds in ActionLet’s think of a different function machine to use in order to calculate the total cost of a CD. Can we simplify the equation that Sasha and Tony derived?

Note: Tony and Sasha used the variable C to represent the original cost of a CD, but I’m using P since it makes more since to call the total cost C and original price P.

Instead of finding the discount and then subtracting it from the original price, why not use the actual % someone pays after the discount is applied? Since the discount here is 28%, someone actually pays 72% of the original price, plus tax and shipping & handling.

For You to DoUse our new function machine to calculate the total cost of each CD from the Patriotic Medley to 90s Favorites and compare to the values you obtained previously.

The final costs should be the same since our function machines, or rules, are equivalent.

For You to DoUse our new function to calculate the total costs of CDs priced between $15 and $20, using increments of $1.

Price Cost

$15 $13.34

$16 $14.10

$17 $14.85

$18 $15.61

$19 $16.34

$20 $17.12

Describe any patterns you see in the table.

The difference between the total cost when each price increases by $1 is not exactly the same, but is close to $0.75.(Note the coefficient of P in the rule above.)

For You to DoTony & Sasha pay 5% tax whether they buy CDs at the music store’s web site or at the mall. Assume that the non-discounted price of each CD is exactly the same on the web site and at the mall store. (Only the web site offers the discount.)

a.At what price is it a better deal to buy a CD on the web site? At the mall store?b.At what price is the final cost of a CD the same from the web site as it is at the mall store?

We can use a rule to program a graphing calculator so that it becomes a function machine that does the calculations for us!

Step 1:Write a rule to represent the cost of buying a CD from each location. Then enter each rule in the graphing calculator as shown.

Step 1:Enter each rule

Step 2: Use the Table feature

Step 3: change the table setup

It’s a better deal on the web site when the price of a CD is more than $6.82. It’s a better deal at the mall store if the price is less than $6.79.

Step 4: Use the Table to compare