Warmup

1
Warm-up

• Solve the following equation
• 13x 2 4 2x 6x

2
Did 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

4
Reminder

• Tutoring/5th block begins today!
• If you need a pass to come to tutoring, let
  me/your other teachers know!

5
Beginning Math I?

• Concept Maps

6
Key Learning

• Students will be able to recognize functions and
  their graphs linear, absolute value, quadratic,
  cubic, radical, and rational

7
Unit Essential Question

• How do I recognize functions and their graphs?

8
Concept 1

• MM1A1.a
• How do we represent functions using function
  notation?
• Vocabulary
• Function notation, equations

9
Concept 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

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Concept 3

• MM1A1.c
• How do we graph transformations of functions?
• Vocabulary
• Transformation, reflection, translation (shift),
  dilation/compression (stretch/shrink), image,
  pre-image

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Concept 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

12
Concept 5

• MM1A1.e
• How do we use graphs and tables to investigate
  behavior of functions?
• Vocabulary
• Function rule, table, graph

13
Concept 6

• MM1A1.f
• How do we recognize sequences as functions with
  domains that are whole numbers?
• Vocabulary
• Sequences, t-table

14
Concept 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

15
Concept 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

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Concept 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

17
MM1A1.a
Representing functions using function notation
Part 1
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Essential Question
MM1A1.a
How do we represent functions using function
notation?
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Let's begin by looking at function notation.
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The 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
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y 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.
22
The 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
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This variable can be anything.
g(a) -a 10
This notation, g(a), indicates we have a
function.
These two must be the same variable.
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Now, you do one. Write the equation p 3q - 6
in funtion notation.
Is there only one right answer?
25
Try these...
1) c -2b 4 2) g 4f - 1 3) x -w 5
Is there only one right answer?
26
Try these...
1) z -2y 4 2) e 4d - 1 3) q -p 5
Is there only one right answer?
27
Teacher, hand out practice sheet
MM1A1.a Function Notation Practice Sheet 1
Turn to next page when ready to check answers.
28
Answers 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
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Functions - Introduction
MM1A1.a
Part 2
Application
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The 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
31
The 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
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Warm-upDay 8
33
Interesting 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

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• 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

35
Solve the equation 4x 2y 8 for y. Write as a
function of x, or y in terms of x.
f(x) 2x 4
36
Solve the equation x y - 9 0 for y. Write as
a function of x (or y in terms of x).
f(x) -x 9
37
Ryan'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
38
Anyone 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
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Teacher, hand out practice sheet.
MM1A1.a Introduction to Functions Practice
Sheet 2
Turn to next page when ready to check answers.
40
Answers 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
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Time for Quiz!
(Quiz in two parts 3 Questions on next page and
then give GPS page 1.)
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Quiz
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.