Title: Warmup
1Warm-up
- Solve the following equation
- 13x 2 4 2x 6x
2Did you know?
- Dartboards are made out of horsehairs.
- Your left lung is smaller than your right lung to
make room for your heart. - 'Crack' gets it name because it crackles when you
smoke it. - Marijuana is Spanish for 'Mary Jane.'
- One of the many Tarzans, Karmuela Searlel, was
mauled to death on the set by a raging elephant. - Slinkys were invented by an airplane mechanic he
was playing with engine parts and realized the
possible secondary use of one of the springs.
3- U.S. Interstates which go north-south are
numbered sequentially starting from the west with
odd numbers, and Interstates which go east-west
are numbered sequentially starting from the south
with even numbers. - Ballroom dancing is a major at Brigham Young
University. - Professional ballerinas use about twelve pairs of
toe shoes per week. - There are 336 dimples on a regulation golf ball.
- A walla-walla scene is one where extras pretend
to be talking in the background -- when they say
"walla-walla" it looks like they are actually
talking. - Cranberry Jell-o is the only jell-o flavor that
comes from real fruit, not artificial flavoring. - Don MacLean's song "American Pie" was written
about Buddy Holly, The Big Bopper, and Ritchie
Valens. All three were on the same plane that
crashed. - The Declaration of Independence was written on
hemp paper
4Reminder
- Tutoring/5th block begins today!
- If you need a pass to come to tutoring, let
me/your other teachers know!
5Beginning Math I?
6Key Learning
- Students will be able to recognize functions and
their graphs linear, absolute value, quadratic,
cubic, radical, and rational
7Unit Essential Question
- How do I recognize functions and their graphs?
8Concept 1
- MM1A1.a
- How do we represent functions using function
notation? - Vocabulary
- Function notation, equations
9Concept 2
- MM1A1.b
- How do we graph and write equation for each of
the Family of Functions? - Vocabulary
- Linear, absolute value, quadratic, cubic,
rational, radical, critical point, slope,
y-intercept, vertex, point of inflection,
starting point, horizontal asymptote, vertical
asymptote, quadrant, parent graph
10Concept 3
- MM1A1.c
- How do we graph transformations of functions?
- Vocabulary
- Transformation, reflection, translation (shift),
dilation/compression (stretch/shrink), image,
pre-image
11Concept 4
- MM1A1.d
- What are the characteristics of a function and
how do you use them? - Vocabulary
- Domain, range, intercepts, zeroes, solutions,
maximum, minimum, vertex form, standard form, end
behavior, increasing, decreasing
12Concept 5
- MM1A1.e
- How do we use graphs and tables to investigate
behavior of functions? - Vocabulary
- Function rule, table, graph
13Concept 6
- MM1A1.f
- How do we recognize sequences as functions with
domains that are whole numbers? - Vocabulary
- Sequences, t-table
14Concept 7
- MM1A1.g
- How do constant rates of change compare to
variable rates of change within the Family of
Functions? - Vocabulary
- Rates of change, variable rates of change
15Concept 8
- MM1A1.h
- How do we determine graphically and algebraically
whether a function has symmetry and whether it is
odd, even, or neither? - Vocabulary
- Symmetry, even, odd
16Concept 9
- MM1A1.i
- How do we interpret an equation in x, and its
solutions as f(x) g(x) and show where they
intersect? - Vocabulary
- Solutions, intersection, parallel, perpendicular
17MM1A1.a
Representing functions using function notation
Part 1
18Essential Question
MM1A1.a
How do we represent functions using function
notation?
19Let's begin by looking at function notation.
20The following equations are written in function
notation.
y 2x 3
b 2a 3
b(a) 2a 3
y(x) 2x 3
b in terms of a
y in terms of x
21y 2x 3
b 2a 3
b(a) 2a 3
y(x) 2x 3
Make a note, the function variable in red can be
anything but, to remain consistent for this
lesson, we will use the variable provided.
22The following equations are written in function
notation.
s 0.5t 1.5
y -4x - 1
s(t) 0.5t 1.5
y(x) -4x - 1
s in terms in t
y in terms of x
23This variable can be anything.
g(a) -a 10
This notation, g(a), indicates we have a
function.
These two must be the same variable.
24Now, you do one. Write the equation p 3q - 6
in funtion notation.
Is there only one right answer?
25Try these...
1) c -2b 4 2) g 4f - 1 3) x -w 5
Is there only one right answer?
26Try these...
1) z -2y 4 2) e 4d - 1 3) q -p 5
Is there only one right answer?
27Teacher, hand out practice sheet
MM1A1.a Function Notation Practice Sheet 1
Turn to next page when ready to check answers.
28Answers to Practice Sheet 1 Introduction to
Functions
Function variable (in red) may vary. 1) y(x)
2x 7
2) c(b) -b - 6 3) p(n) -4
7n 4) z(y) -y 7 5) b(a) 3a - 4 6)
f(g) -4 7g
8) c(b) 10 4b 11) p(e) 2e - 4
7) y(x) 4 - 4x 10) z(y) -5 - 7y
9) g(h) 2h - 7 12) m(n) 4 - n
29Functions - Introduction
MM1A1.a
Part 2
Application
30The Anderson Family is comparing the costs of
two different satellite companies. With plan A,
equipment installation is 199, and the monthly
fee is 29. With plan B, the installation is
100, and the monthly fee is 50. Write the
function rule for both plans.
Plan A is s(m) 29m 199 Plan B is s(m)
50m 100
31The directions on the label of a ham tell you to
cook the ham 45 minutes per pound. Write the
function rule in function notation for this
situation, where p is the number of pounds.
h(p) 45p
32Warm-upDay 8
33Interesting Facts
- In ancient Rome, it was considered a sign of
leadership to be born with a crooked nose - The word "checkmate" in chess comes from the
Persian phrase "Shah-Mat," which means the king
is dead - If you yelled for 8 years, 7 months and 6 days,
you would have produced enough sound energy to
heat one cup of coffee - A common drink for Tibetans is Butter Tea which
is made out of butter, salt, and brick tea
34- Bourbon was first made by a Baptist minister from
Bourbon County in Kentucky in 1789. That is where
it got its name - The Pentagon, in Arlington, Virginia, has twice
as many bathrooms as is necessary. When it was
built in the 1940s, the state of Virginia still
had segregation laws requiring separate toilet
facilities for blacks and whites - McDonald restaurants serve food and drink to an
amazing 43 million customers on a daily basis - The game Monopoly was once very popular in Cuba
however, Fidel Castro ordered that all games be
destroyed - Nearly half of all Americans suffer from symptoms
of burnout
35Solve the equation 4x 2y 8 for y. Write as a
function of x, or y in terms of x.
f(x) 2x 4
36Solve the equation x y - 9 0 for y. Write as
a function of x (or y in terms of x).
f(x) -x 9
37Ryan's Steak House offers a buffet at lunch for
5.99 per person. Write the function rule that
shows the cost of your group where p is the
number of people in your group.
C(p) 5.99p
38Anyone visiting Bull Rider's Club will pay a
cover charge of 10 and then they can buy
appetizers while they are there for 3 each.
Write the function rule that shows the cost of
your visit to this sports club. (A cover charge
is a fee charged to enter the door.)
C(a) 3a 10
39Teacher, hand out practice sheet.
MM1A1.a Introduction to Functions Practice
Sheet 2
Turn to next page when ready to check answers.
40Answers to Practice Sheet 2 Introduction to
Functions
1) Magic Kingdom Plan is t(p) 225p 1250
Universal Studios Plan is t(p) 175p
1300 2) C(p) 10.50p 3) a. y x - 10
b. y 7 - 2x
41Time for Quiz!
(Quiz in two parts 3 Questions on next page and
then give GPS page 1.)
42Quiz
1) Write x w 7 in function notation.
2) Write z 9 - 2a in function notation.
3) Write b - 5a - 10 in function notation.
Now, take quiz on GPS page 1.