Transcript Unit 2- Interpreting Functions

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 Functions
A. 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:
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Domain
Range
End Behavior
Minimum(s)
Maximum(s)
X-Intercepts (roots)
Y-Intercept
Asymptotes
Axis of Symmetry
Can you Name the Function?
B. Examples
① Given the function below list all the key features
applicable. What type of function is this?
B. Examples
② Given the function below list all the key features
applicable. What type of function is this?
B. Examples
③ 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-toone)
④ A relation is any set of points that is NOT one-toone
B. Notation
 Domain and range can be written:

Algebraically

Using Interval Notation

Described Verbally (graphically)
C. Examples
① 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. Examples
① 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. Examples
② State the domain and range of the function.
What type of function is this?
C. Examples
③ State the domain and range of the function.
What type of function is this?
C. Examples
④ State the domain and range of the function.
What type of function is this?
C. Examples
⑤ 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 Function
Y-Intercept: (0, 5)
End Behavior:
X
+ then y
+
Domain: All real numbers
Range: 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 Options
Unit 2
Functions
ALL Key Features
Worksheet
(Half sheet)
Unit 1
Normal Curve
Worksheet
(Full Page)
I’m Totally Good!!!
Create a
mathematical
argument…
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. Examples
①Define 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 function
2) 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=input
② Range=y-values=output
③ 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
① g(-3)
g(x)= 8x-1
h(x)=|x-6|-9
Evaluate the function for the given inputs
f(x)= -x2+3x-1
② h(4)
g(x)= 8x-1
h(x)=|x-6|-9
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
③ x= -4
g(x)= 8x-1
h(x)=|x-6|-9
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 Options
Unit 1
Standardizing
Normal Curve
Unit 2
LT 2D Piecewise
Functions
I’m Totally Good!!!
Evaluating
Functions
School Website
LT 1C-Worksheet
Worksheet
w/graphs
Worksheet
Homework Help?
Unit 1 Click on Learning Target Links
Watch Videos on LT 1C
Khan 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 functions
o 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
Word
Category 3
Category 1
Word
Word
Word
Most Important
Word
Word
Word
Word
Word
Category 2
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 below
Level A
Level B
Level C
State the
Domain and
Range!
Level A
Level C
Level B