A number is inputted into a magic box, which then outputs a different number.

Using the table below, what does the magic box do to the input number to get the output number?

Warm-Up: December 5, 2014

Input -2 -1 2 3 5

Output 1 -2 1 6 22

Functions – The Basics

Investigation 5AAdvanced Integrated Math I

Practice finding the rule to describe a set of input and output values.

Goal for Today

Mr. Szwast will think of a rule. You will tell Mr. Szwast the input, and then

he will tell you the output. You then get to guess what the rule is.

Game Time

You will work with your partner. One person will be the Rule Maker, the other will be the Rule Guesser.

The Rule Maker must decide on a rule (simple enough that they can do the calculations in their head).

The Rule Guesser gives an input number to the Rule Maker. The Rule Maker gives the output value.

The Rule Guesser tries to guess the rule. Your score is the sum of the number of input values used and the number of rule guesses.

Switch roles with your partner and repeat. Low score wins!

Your Turn!

Read pages 362-364 Page 364 #7-10

Assignment

Pick up a handout: “5.02 – Building Functions”

Read the front page and complete the table with your partner.◦ You may use a calculator.

Finish reading the rest of the handout. Complete #2

Warm-Up: December 8, 2014

Homework Questions?

Tables on TI-83/TI-84

Use Sasha and Tony’s rule from the handout. Find the total costs of CD’s priced between $15 and $20. Use price increments of $1.

3. Describe any patterns in the table.4. Find a simpler rule than Tony and Sasha’s rule that

agrees with the table.5. Tony and Sasha pay 5% sales tax whether they

buy CD’s at the mall or the music store web site. Assume that the nondiscounted price of each CD is exactly the same at the mall and at the music store web site.

a) At what price is it a better deal to buy a CD at the music store web site? At the mall?

b) At what price is the final cost of a CD the same at the music store web site and at the mall?

You-Trys (with partner)

Page 370 #6, 7, 8, 12, 14

Assignment

Page 370

See textbook for #8 and #14.

Tony and Sasha are playing the Guess My Rule game.

In round 1, Tony is the Rule Maker.

a) When Tony uses a fair rule, what is the value of c?b) How are the variables a and b related?c) Do you have enough information to find the value

of a?

Warm-Up: December 9, 2014

Sasha’s Input Tony’s Output

1 1 returns a

2 2 returns 7

5 5 returns 11

1 1 returns b

2 2 returns c

Homework Questions

Tony and Sasha are playing the Guess My Rule game.

In round 2, Sasha is the Rule Maker.

Tony says, “That rule’s not fair!” What makes Tony say that?

Think-Pair-Share

Tony’s Input Sasha’s Output

1 1 produces 5

2 2 produces 3

3 3 produces 25

1 1 produces 11

Is It a Function?Section 5.03

Advanced Integrated Math I

How can we determine if a relationship is a function?

Essential Question

The Function Machine

Add 2 to the input…

An Unfair RuleAdd 2 or 3 depending on a coin flip

A function is a rule that assigns each input to exactly one output.

Functions

Does the rule “Add 4 to the input and square the result” define a function?

Think-Pair-Share

Does the rule “Find a number that is less than the input” define a function?

Think-Pair-Share

Give three examples of rules that define functions and three examples of rules that do not define functions.

You-Try (with partner)

Read pages 372-374 Page 376 #5-9, 12

Assignment

Page 376

1. What is the input?2. What is the name of the function?3. What is the output?4. What would the output be if the input were

3?

Warm-Up: December 10, 2014

Homework Questions?

Covers Chapters 1-3

District Benchmark Tomorrow

Naming FunctionsSection 5.04

Advanced Integrated Math I

How do we evaluate functions and compositions of functions?

Essential Question

The function f is defined by Evaluate each of the following

You-Try122 xxx

f

xff

fafe

afd

fc

fb

fa

)

7)

7)

)

3)

1)

We can give a function any name we want. We can use transformation notation or

function notation to write a function.

Function Names

We can take the output of one function, and make it the input of another function. This is called the composition of functions.

Compositions of Functions

Example: Find f(g(5))

3

122 x

xgxxxf

Example: Find g(f(5))

3

122 x

xgxxxf

Read pages 378-379 Page 381 #6-12

Assignment

Page 381

Have your page 376 assignment out for Mr. Szwast to check.

After your homework is checked, clear everything off of your desk except pencils, erasers, and a non-graphing calculator.◦ If you would like to borrow a calculator, pick one

up now.

December 11, 2014District Benchmark Assessment

You will not receive extra time after class (except for IEP or 504), so use your time wisely.

Write your name and the date on the front page. You will receive a bubble sheet after you receive

your test. #1-6 are multiple select – there could be more

than one correct answer. You must choose all of the correct options. Record your answers on the bubble sheet.

Write your answers to #7-12 on the test. When finished, put your bubble sheet inside your

test and turn it in to Mr. Szwast

December 11, 2014District Benchmark Assessment

What inputs do not work in the function ?

Warm-Up: December 12, 2014

xx

1

If you did not take the Chapter 4 Test or the District Benchmark, you can take either (or both) today after school, in this room.

Test Make-Ups

You will have one opportunity to retake each test in January.◦ Each test will be offered on one specific day at a specific

time. This is the only time you may retake it. Before retaking, you must do all 3 of the

following:◦ Get your previous test signed by a parent/guardian◦ Complete all missing/incomplete assignments from the

chapter◦ Complete test corrections following the assigned format.

Eac

Chapters 1-3 Test Retakes

Chapter 1: Wednesday, January 7, 2:45-3:45 Chapter 2: Wednesday, January 14, 2:45-3:45 Chapter 3: Wednesday, January 21, 2:45-3:45

If you show up late, you may still retake it, but you must turn in your test by 3:45.

Signed test, test corrections, and missing homework assignments are due in class on Tuesday, the day before each test.

Chapters 1-3 Test Retakes

Homework Questions?

Function Inputs and Outputs

Section 5.05Advanced Integrated Math I

How do we find the domain of a function?

Essential Question

The set of inputs is called the domain of the function.

The set of outputs that a function produces is called the range of the function.

Definitions

1. What is the domain?2. What is the range?

A Juicer

1. What is the domain?2. What is the range?

Library Catalog System

Identify the domain and range for each:1. The salary of a worker is a function of his or

her skill level.2. The price of an advertisement during a

television show is a function of the number of viewers.

3. The magnitude of a sonic boom is a function of an airplane’s weight and fuselage length.

You-Try (with partner)

What is the domain of the following function?

Example

5xx

x

Find the domain of each of the following functions.

You-Try (with partner)

number primeth )44

37526)3

12

513)2

2

1)1

2

2

xxx

xxx

x

xx

xx

Read pages 383-384 Page 386 #7-10, 12

Bring your textbook on Monday◦ If you have a smartphone, you may instead take

pictures of pages 387-397 and use that in class on Monday.

Assignment

Page 386

Write the equation of the line, in slope-intercept form, that passes through (-1, 2) and (2, 6).

Warm-Up: December 15, 2014

Homework Questions?

Graphing FunctionsSection 5.06

Advanced Integrated Math I

What can we learn about relations from their graphs?

Essential Question

Read the “Minds in Action” on pages 387-388. Play three rounds of the Guess My Rule game

against your partner using Tony’s graphing method.◦ Each person is the Rule Maker 3 times and each

person is the Rule Guesser 3 times. With your partner, answer “For Discussion”

#2, 3 on page 388 Read the “Minds in Action” on page 389 With your partner, answer “For Discussion” #4

on page 390

Directions

2) The y-coordinate of the intersection point gives the value of f(-2), which is 8. f(0)=3

3) 0.5 and 5.54) Graphs 2 and 4 are functions; graph 1 is

not a function.Explain vertical line testExamples of functions and non-functions:

Answers

Page 392 #8, 9, 12, 13, 16-18

Page 396 #1-7

Assignments