Welcome to the First Day of…
BLOCK SCHEDULE!!!
Please do the following:
1) Pick up an Assignment List and Entry Ticket from the side shelf .
2) If you have your signed syllabus please take it out.
3) Take out U1L1 and U1L2 Notes and a pencil.
4) Begin Entry Ticket.
Welcome to the First Day of…
BLOCK SCHEDULE!!!
Homework:
o Get Syllabus signed by Monday
o Hw #1 pg. 10 #’s 22-34 even, 38, 39, 44-50 even
Hw #2 pg. 17 #’s 13, 19-27 odd  Write in the 2nd
o Updates: Materials Quiz is Monday
Unit 1 Quiz 1 (1.1-1.2)
 Write in the 1st box on
Assignment List
Agenda
1)
2)
3)
4)
5)
6)
7)
Collect Syllabus
Entry Ticket (4-5 minutes)
Relations and Functions
1st / 5th / 6th Period Book Room (8:45) / (2:15) / (2:05)
**Calculator Activity**
Composition of Functions
Cool-Down
Entry Ticket
Using equity sticks, some of you will be called to the document camera
to share your entry ticket solutions.
What I expect when you present:
o To speak clear and loud enough for all to hear.
o To speak with confidence.
o To answer, to the best of your ability, any questions that are asked.
o To be proud of yourself regardless if the answer is correct or
incorrect.
Make corrections in a different colored pen!
Turn in entry tickets at the end of each period; Not Now.
Entry ticket and Participation Points.
Learning Objective U1L1
By the end of this period you will be able to:
o Determine whether a given relation is a function and identify
the domain and range.
Relations and Functions
Roster Notation
o Listing all the data of a set.
o The data is listed in braces and separated by commas.
o Example: Put the numbers 8, 21, 43, and 15 in roster notation.
{8, 15, 21, 43}
Inequalities Set Notation
o Describing an interval that is continuous for some time using the
inequality symbols. Open dots exclude endpoints and closed dots
include endpoints.
o Example:
-1 < x < 1
2<x<∞
Relations and Functions
Interval Notation
o Describing an interval that is continuous for some time using a
bracket to include endpoints and parentheses to exclude
endpoints.
o Example:
(-1, 1) U (2, ∞)
Set Builder Notation
o A combination of roster and inequality set notation.
o Example:
Relations and Functions
Data sets as we see come in various forms so lets look at a real life data
set in the form of a table.
Take 1 minute to discuss in your groups, what the table is trying to tell
us.
(a) The table below shows the pounds per square inch (psi) of pressure
that push on a body at various water depths.
(1) Practice: State the relation, domain,
and range of the data as a set of
ordered pairs.
**You may not remember all vocab.
words; try the best you can 
Relations and Functions
Relation
o Set of ordered pairs.
Domain
o The set of all x’s of the ordered pairs.
o Commonly represented by the letter D.
Range
o The set of all y’s of the ordered pairs.
o Commonly represented by the letter R.
Relations and Functions
 In your clusters discuss the following: is the relation from (1) a function?
Have evidence to support your conclusion.
Function
o A relation in which each x-value is paired with exactly one y-value.
Lets graph the function on our graphing calculators!
To Enter Data Points: STAT
EDIT
{in L1 enter the x’s; in L2 enter the y’s}
2nd Y=
1:
ON {Type should be scatter plot or all dots}
ZOOM
9: ZOOM STAT
Relations and Functions
 We have already mentioned that this is a function. What would it
have to look like in order to NOT be a function?
Function
o A relation in which each x-value is paired with exactly one y-value.
o Must pass the vertical line test.
• If every vertical line drawn on the graph of a relation passes
through no more than one point of the graph, then the relation is
a function.
Now you all are knowledgeable about Relations, Domain and Range,
and Functions. Take 5 minutes to complete Practice 2-4. You may work
with your tablemates.
Relations and Functions
(2) Practice: Determine if the set is a function, and state the domain
and range of the relation.
(a) { (1, 3), (2, 5), (4, 8), (5, 10) }
(b) { (2, 6), (3, 7), (3, 10), (5, 21) }
Relations and Functions
(3) Practice: State if the graphs are functions.
(a)
(d)
(b)
(c)
Relations and Functions
(4) Practice: Given that x is an integer, state the relation representing
each equation by making a table of values. Then graph the ordered
pairs of the relation.
(a) y = 3x + 5 and -3 < x ≤ 1
(b) y = -5 and 1 ≤ x ≤ 5
Relations and Functions
Function Notation
o Represented by f(x) and read as f of x.
(5) Practice: Evaluate the function, f(x) = 7 – x2, for the given values.
(a) f(2a)
(b) f(-3)
Relations and Functions
(6) Practice: State the domain of each function.
(a)
(b)
Note:
o Any value that makes the denominator 0 must be excluded.
o Any value that makes the radicand negative or 0 (when it is not in
the denominator) must be excluded.
**Calculator Activity**
I understand how drained you all must be at this moment so let’s take a
mini break from the lesson and get to know our calculators.
I am going to give you 10 minutes to complete the calculator activity. If
you need help finding keys on your calculator please ask your
tablemates. If you need extra assistance please talk to me!
*** Write notes on your worksheet to help you remember where the
keys are!
Learning Objective U1L2 (1.2)
By the end of this period you will be able to:
o Perform operations with functions and find composite
functions.
Composition of Functions
Operations of Functions
Sum: (f + g)(x) = f(x) + g(x)
Difference: (f - g)(x) = f(x) - g(x)
Product: (f  g)(x) = f(x)  g(x)
Quotient: (f / g)(x) = f(x) / g(x) , where g(x) ≠ 0
With your tablemates, predict what each operation will look like when
expanded.
Composition of Functions
(1) Practice: Given f(x) = x + 1 and g(x) = x2, find each of the following:
(a) (f + g)(x)
(b) (g - f)(x)
(c) (g  g)(x)
(d) (f / g)(x)
Composition of Functions
Composition of Functions
(f  g)(x) = f( g(x) )
(g  f)(x) = g( f(x) )
o Process where we substitute an entire function into another function.
How could this operation be expanded?
Composition of Functions
(1) Practice: Given f(x) = x + 1 and g(x) = x2. Simplify your final answer.
(e) (g  f)(x)
(f) (f  f)(x)
Composition of Functions
(2) Practice: State the domain of (f  g)(x) for f(x) =
g(x) =
and
How can you check to see if your final domain is correct?
Composition of Functions continued…
o The domain of f  g includes all of the elements x in the domain of g
for which g(x) is in the domain of f.
o A composition of function is called an iteration, meaning taking the
output and plugging it back in.
Composition of Functions
(3) Practice: Find the first three iterates, x1, x2, and x3, of the function
f(x) = 3x + 2 for an initial value of x0 = 4.
Knowing the definition of an iteration, how do you plan to find x1?
Cool Down…
The cool down combines all that we have learned today in an interactive
way!
Step 1: Go to someone not in your table and have them write an
equation for f(x) then go to a different person not from your table and
have them write an equation for g(x). Lastly, find a third person to tell
you the operation for which you are to use.
Step 2: Return to your seat and using the f(x) and g(x) you were given
simplify using the specified operation.
Step 3: Find the domain of your simplified equation.
Cool Down…
Step 4: Determine if your simplified equation is a function and explain
(you may using a graphing calculator).
Step 5: Answer the challenge question. I challenge you to figure it out 
Please place all Entry Tickets in the middle of your table; I will come
around at the end of class to collect them.
Table Share
I will give you 20 seconds to discuss with your cluster-mates then I will
clap twice to signal that I need your attention.
 If you want to know what the homework is for the day, what can you
do?
 You were absent and want to turn in the homework. What do you
do?
 Your desk is dirty and you want to clean it. Ms. Swenson has Clorox
wipes on her desk. What will you do?