Unit 2- Interpreting Functions

2A- I can use technology to graph a function and analyze the graph to

describe relevant key features (End Behavior, Domain, Range, Min/Max,

x-& y- intercept)

I. Analyzing Graphs of FunctionsA. Key Features of Graphs

① Every type of function has its own unique set of key features which can include vertical and horizontal asymptotes as well as axis of symmetry

② When analyzing ALL functions the key features include:• Domain• Range• End Behavior• Minimum(s)• Maximum(s)• X-Intercepts (roots)• Y-Intercept• Asymptotes• Axis of Symmetry

Can you Name the Function?

B. Examples① Given the function below list all the key features

applicable. What type of function is this?

B. Examples② Given the function below list all the key features

applicable. What type of function is this?

B. Examples③ Given the function below list all the key features

applicable. What type of function is this?

Functions Scavenger Hunt• With a partner– Must travel around the room together– Both complete the graphic organizer

• Symbol & Fill in the blanks– Don’t give answers away to other groups

• Symbols are on the top left

• Should hear academic vocabulary (cubic, quadratic, maximum, x-intercept, …)

Exit Slip

What are all the key features of the normal curve?

Unit 2- Interpreting Functions

2C- I can define a function and describe its Domain and Range

graphically, algebraically and numerically and interpret the domain

and range for a given situation

Unique Function

• What function is he using to represent the situation he is describing?

• What key features does his function have?

• What is the Domain & Range of his function?

II. Domain and Range of Functions A. Definitions

① The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function.

② The range is the set of all possible output values (usually the variable y, or sometimes expressed as f(x)), which result from using a particular function

③ A function is a set of point in which all domains are paired with exactly one range (called one-to-one)

④ A relation is any set of points that is NOT one-to-one

B. Notation Domain and range can be written:

Algebraically

Using Interval Notation

Described Verbally (graphically)

C. Examples① Algebra I-State the domain and range of the set of

points below. Is the set of points a relation or a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

C. Examples① Algebra I-State the domain and range of the set of

points below. Is the set of points a relation or a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

C. Examples② State the domain and range of the function. What

type of function is this?

C. Examples③ State the domain and range of the function. What

type of function is this?

C. Examples④ State the domain and range of the function. What

type of function is this?

C. Examples⑤ State the domain and range of the function. What

type of function is this?

List all Key Features of the function given below (name the function).

Square Root FunctionY-Intercept: (0, 5)End Behavior:X + then y +Domain: All real numbersRange: y ≥ 5

If you Roll… • 0 Determine Domain and Range of the function and write in

algebraic form

• 1 Determine the End Behavior of the function

• 2 Analyze the function for ALL key features

• 3 Find any three key features of the function

• 4 Determine Domain and Range of the function and write in interval notation

• 5 Determine the End Behavior of the function

Homework OptionsUnit 2

FunctionsALL Key Features

Unit 1 Normal Curve

I’m Totally Good!!!Create a

mathematical argument…

Worksheet (Half sheet)

Worksheet(Full Page)

Pg. 63 (59-61)

Homework Help?Khan Academy

Unit 2 Search “Domain and Range from Graphs”Watch Video & Do Problems

Unit 1 Search “68 95 99.7 Rule”Watch Video & Do Problems (Empirical Rule)

Graph Each Function and Analyze all Key Features

Level A Level B Level C

Unit 2- Interpreting Functions

2D-I can describe relevant key features of piece-wise functions,

explain how the constraints determine the domain, use the

constraints to evaluate the function and graph linear piece-wise functions.

III. Piecewise Functions

A. In real life, most situations cannot be represented using only one function.

B. A piecewise function is a function that is defined on a sequence of intervals/domains

C. Examples①Define the domains in the piecewise function

and explain what any key features represent.

②The function below represents parking lot rates near UCLA during the week. Define the domains in the piecewise function and explain what any key features represent.

③The function below represents Jessica’s climb to the top of a waterslide and then her decent. Define the domains in the piecewise function and explain what any key features represent.

④Define the functions and their domains in the piecewise function below. What is the range of the function?

Define the functions and their domains in the piecewise function below. What is the range of the function?

1) Define the domains for this piecewise function

2) Identify the key features of this piecewise function

Together:1) Create a story that goes with this function2) What do the key features mean within the

context of your story?

Galley Walk

• Pink papers around the room

• Level A-B-C

• Answers on back; check your work & explanations

FYI-Upcoming…• Tutoring with DeVeny– Tuesday 7am– Thursday 7am

• Afterschool tutoring– Mon-Thur 2:45-4:00 BAYLIS rm 607

• Test next week (T or W)– Unit 1 AND Unit 2

IV. Evaluating Functions

A. Reminder: All functions have a domain and a range.

B. Vocabulary:① Domain=x-values=input② Range=y-values=output③ Evaluating a function is when a given input is

placed into a function and the output is determined

C. Examples

Evaluate the function for the given inputs

f(x)= -x2+3x-1 g(x)= 8x-1 h(x)=|x-6|-9

① g(-3)

Evaluate the function for the given inputs

f(x)= -x2+3x-1 g(x)= 8x-1 h(x)=|x-6|-9

② h(4)

Evaluate the function for the given value of x

① f(2)

Evaluate the function for the given value of x

② m(-8)

Evaluate the function for the given value of x

③ m(10)

Evaluate the function for the given value of x

④ f(0)

Evaluate the function for the given inputs

f(x)= -x2+3x-1 g(x)= 8x-1 h(x)=|x-6|-9

③ x= -4

Sideways

• Complete a problem

• Find your answer– Can’t find it? Check for a mistake!

• Move SIDEWAYS for a new problem

Error Analysis

• What type of error (if any) did you make?– Mark exit ticket with type of error– Write sentence about what was missing/wrong

• Log levels onto learning target logs

Quick Check

The scores on the chapter 3 exam in Alex’s history class were normally distributed with a mean of 71 and a standard deviation of 5. Alex scored a 74. He knows that his parents will not be happy; thus, his plan is to use what he learned in Algebra II and explain to his parents that he scored higher than 60% of his class. Is Alex’s statement accurate? Explain why or why not.

Alex’s statement is not correct. He is getting the z-score associated with his test confused with the actual area under the normal curve.Z=Alex’s z-score is 0.60 but this does not mean that he scored better than 60% of his class. 0.60 is the z-score needed to look up the percentage of students who scored lower than him using the z-table. A z-score of 0.60 gives an area of 0.7257; thus Alex actually scored higher than about 73% of the students in the class.

Homework OptionsUnit 1

Standardizing Normal Curve

Unit 2 LT 2D Piecewise

Functions

I’m Totally Good!!!Evaluating Functions

School WebsiteLT 1C-Worksheet

Worksheet w/graphs

Worksheet

Homework Help?Unit 1 Click on Learning Target Links

Watch Videos on LT 1CKhan Academy

Unit 2 Search “Domain and Range from Graphs”Watch Video & Do Problems

V. Graphing Linear Piecewise Functions

A. The domain is VERY important when graphing piecewise functionso Open circle the domain value is not included (not

equal to)• Closed circle the domain value is included (equal

to)B. To graph a linear piecewise function graph

each “piece” of the piecewise function and them apply the given domain to each linear function

Prior Knowledge Check (Algebra I)On Your OWN Graph…

① y=8x-9

②-6x+4y=-36

③-10y=5x+20

Prior Knowledge Check (Algebra I)Together: What was your APPROACH to

graphing each line?

① y=8x-9

②-6x+4y=-36

③-10y=5x+20

Prior: Graphing Linear Equations

C. Examples-Graph each function and state the domain and range in interval notation

①

C. Examples-Graph each function and state the domain and range in interval notation

②

C. Examples-Graph each function and state the domain and range in interval notation

③

Whiteboards

• List every word you think is an “important” word from Unit 2

Whiteboards

• List every word you think is an “important” word from Unit 2

• Pick the ONE word you think is THE most “important” Write that word on a post-it and explain why it’s the most important

Whiteboards

• List every word you think is an “important” word from Unit 2

• Pick the ONE word you think is THE most “important” Write that word on a post-it and explain why it’s the most important

Post-Its

• TOGETHER compare lists and create a post-it for every word

• Agree on THE most important word

• Take all the post-its and put them into categories (if you have to use a word more than once because it goes into more than one category make another post-it)

Create a Concept Map Unit 2

Most Important Word

Category 1

Category 2

Category 3

Word

Word

Word

Word

Word

Word

Word

Word

Word

Take a Picture of Your Map

• Homework: Create your own version of the Map– Add at least two connections onto YOUR map that

you and your team didn’t come up with

Graph one of the functions belowLevel A

Level B

Level C

State the Domain and

Range!

Level A Level B

Level C