Integrated Math I: Function Basics and Building Functions

1. 5.01 Getting Started
(Functions—The Basics)
Chapter 5
Exponents and Functions

2. 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.

3. 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.

4. 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

5. 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.

6. For You to Explore
Turn 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.

7. For You to Explore
Turn 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.

8. One More “Guess My Rule” Game
3 is added to each input, or “x returns x + 3.”

9. 5.02 Building Functions
Chapter 5
Exponents and Functions

10. Minds in Action
Turn 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.

11. Minds in Action
Turn 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.

12. Minds in Action
Let’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.

13. For You to Do
Use 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.

14. For You to Do
Use 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.)

15. For You to Do
Tony & 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!

16. 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.

17. Step 1:
Enter
each rule

18. Step 2: Use
the Table
feature

19. Step 3:
change
the
table
setup

20. 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