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Warmup

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One of the many Tarzans, Karmuela Searlel, was mauled to death on the set by a raging elephant. ... and tables to investigate behavior of functions? Vocabulary: ... – PowerPoint PPT presentation

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Title: 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

10
Concept 3
  • MM1A1.c
  • How do we graph transformations of functions?
  • Vocabulary
  • Transformation, reflection, translation (shift),
    dilation/compression (stretch/shrink), image,
    pre-image

11
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

16
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
18
Essential Question
MM1A1.a
How do we represent functions using function
notation?
19
Let's begin by looking at function notation.
20
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
21
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
23
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.
24
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
29
Functions - Introduction
MM1A1.a
Part 2
Application
30
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
32
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

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

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
39
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
41
Time for Quiz!
(Quiz in two parts 3 Questions on next page and
then give GPS page 1.)
42
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.
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