# Math 1 Unit 1 Functions

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### Warm-up :

Warm-up Solve the following equation: 13x – 2 = 4 + 2x – 6x

### Did you know? :

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.

### Slide 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

### Reminder :

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

### Beginning Math I :

Beginning Math I Concept Maps

### Key Learning :

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

### Unit Essential Question :

Unit Essential Question How do I recognize functions and their graphs?

### Concept 1 :

Concept 1 MM1A1.a How do we represent functions using function notation? Vocabulary: Function notation, equations

### Concept 2 :

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

### Concept 3 :

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

### Concept 4 :

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

### Concept 5 :

Concept 5 MM1A1.e How do we use graphs and tables to investigate behavior of functions? Vocabulary: Function rule, table, graph

### Concept 6 :

Concept 6 MM1A1.f How do we recognize sequences as functions with domains that are whole numbers? Vocabulary: Sequences, t-table

### Concept 7 :

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

### Concept 8 :

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

### Concept 9 :

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

### Slide 17:

Representing functions using function notation MM1A1.a Part 1

### Slide 18:

Essential Question How do we represent functions using function notation? MM1A1.a

### Slide 19:

Let's begin by looking at function notation.

### Slide 20:

The following equations are written in function notation. y(x) = 2x + 3 y = 2x + 3 b = 2a + 3 b(a) = 2a + 3 y in terms of x b in terms of a

### Slide 21:

y(x) = 2x + 3 y = 2x + 3 b = 2a + 3 b(a) = 2a + 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.

### Slide 22:

The following equations are written in function notation. y(x) = -4x - 1 y = -4x - 1 s = 0.5t + 1.5 s(t) = 0.5t + 1.5 y in terms of x s in terms in t

### Slide 23:

g(a) = -a + 10 This notation, g(a), indicates we have a function. These two must be the same variable. This variable can be anything.

### Slide 24:

Now, you do one. Write the equation p = 3q - 6 in funtion notation. Is there only one right answer?

### Slide 25:

Try these... Is there only one right answer? 1) c = -2b + 4 2) g = 4f - 1 3) x = -w + 5

### Slide 26:

Try these... Is there only one right answer? 1) z = -2y + 4 2) e = 4d - 1 3) q = -p + 5

### Slide 27:

Teacher, hand out practice sheet: MM1A1.a Function Notation Practice Sheet 1 Turn to next page when ready to check answers.

### Slide 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 7) y(x) = 4 - 4x 10) z(y) = -5 - 7y 8) c(b) = 10 + 4b 11) p(e) = 2e - 4 9) g(h) = 2h - 7 12) m(n) = 4 - n

### Slide 29:

Functions - Introduction MM1A1.a Part 2 Application

### Slide 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

### Slide 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

Warm-upDay 8

### Interesting Facts :

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

### Slide 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

### Slide 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

### Slide 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

### Slide 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

### Slide 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

### Slide 39:

Teacher, hand out practice sheet. MM1A1.a Introduction to Functions Practice Sheet 2 Turn to next page when ready to check answers.

### Slide 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

### Slide 41:

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

### Slide 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.