TAKING NOTES

DATE / UNIT / SECTION

WRITE EVERYTHING UNLESS TOLD OTHERWISE

REMEMBER EVERYTHING

YOU WILL NEED A GRAPH PAPER (NOTEBOOK PERFERRED FOR ORGANIZATION PURPOSES) BEGINNING FRIDAY

UNIT 1

FUNCTIONS

1-1 September 9th

Function Introduction

SWBAT identify the subsets of real numbers.

SWBAT contrast a continuous system and a discrete system

SWBAT represent a set of numbers using set builder notation.

SWBAT represent a set of numbers using interval notation.

Subset of Real Numbers

Letter

Set Examples

R real All examples below

I irrationals

Q rationals -2, 0.125, ,

Z integers -1000, 95, 2, -7, 3, -5

W wholes 0, 1, 2, 3, 4, 5, 6…

N naturals 1, 2, 3, 4, 5, 6, 7… What about zero?

What is the smallest value of x such that x > 1…If x is an integer ?

If x is a real number ?

What is the largest value of t such that…

t < 6.5 t < -4

If t is a real number?

If t is an integer?

If t is a whole number?

If t is a real number?

If t is an integer?

If t is a whole number?

Continuous or Discrete System

Continuous System Discrete System

Give examples of…

A continuous system

Such as…

Distance as a function of time

A discrete system

Such as…

Number of people in a room

SET BUILDER NOTATION

Lets say “x is a natural number greater than 5”

{ x \

The set of numbers x such that…

x is greater than 5…

x > 5

, x N}

and x is an element of the set of natural

numbers.

SET BUILDER NOTATION VOCAB

Exclusive

An exclusive set of numbers does not include the endpoint(s) of the set

Such as…

8 > x > 4

Inclusive

An inclusive set of numbers does include the endpoint(s) of a set

Such as…

8 ≥ x ≥ 4

Describe each set of real numbers using set builder notation1. t is all whole numbers greater than or equal to 8

2. d is all integers between 2 and 4, exclusive

3. s is all real numbers between -4 and 7, inclusive

4. m is all irrational numbers greater than 1

5. x is all multiples of 4

1. { t | t ≥ 8, t }

2. {d | 2 < d < 4, d

3. { s | -4 ≤ s ≤ 7, s

4. { m | m > 1, m

5. { x | nx, n

INTERVAL NOTATION

[ or (

22 < x ≤ 43 is represented in interval notation as…

[22, 43) because 22 is not included but 43 is included

UNION

x ≤ -16 or x > 5

(-∞, -16) U [5, ∞)

Describe each set using interval notation

1. -8 < x ≤ 16

2. x < 11

3. x < 8 or x > 15

4. d ≥ -5

1. [-8, 16)

2. (- , 11]

3. (-∞,8] U [15, ∞)

4. (-5,∞)

EXIT TICKET – SEP 9th

1. Write a number between -2 and 2 that is a whole number.2. Write a non-whole number between -2 and 2 that is an integer.3. Write a non-integer between -2 and 2 that is a rational number.4. Write a non-rational number between -2 and 2 that is a real

number.5. Give an example of a continuous system and a discrete system.6. Represent “x is all integers between 3 and 9, inclusive” using set

builder notation.7. Represent “x > -22 or x ≤ -35” using interval notation

UNIT 1

FUNCTIONS

1-1 September 10th

Function Introduction

SWBAT utilize the vertical line test to determine if a graph is a function

SWBAT write a function in function notation

SWBAT identify the input and output of a function in function notation

SWBAT evaluate a function notation with non-numerical inputs

FUNCTION?

VERTICAL LINE TEST

A vertical line represents a single input extended vertically to both infinities (such as x=3).

A function can only have one output for each unique input.

If any vertical line hits the graph at more than one point, the the graph is not function (an unique input has more than one output).

If no vertical line hits the graph at more than one point, the graph is a function (each unique input has only one output).

FUNCTION?

Function Notation

In function notation, the symbol f(x) is read f of x and interpreted as the value of the function f at x.

If the equation is y = 6x, the related function is f(x) = 6x .

So y = f(x), don’t be surprised when it is written this way.

Function Input and Output

Input

For the function f(x), the input is represented by x.

For the function d(t), the input is represented by t.

The set of all inputs is the domain.

The input is the independent variable.

Output

For the function f(x), the output is represent by f(x).

For the function d(t), the output is represented by d(t).

The set of all outputs is the range.

The output is the dependent variable.

REPRESENT, REPRESENT!

1. Represent in function notation a function for which the output is always three less than the input.

2. Represent in function notation a function for which the output is always two more than three times the input squared.

3. Represent in function notation a function for which the output is always three more than the square root of the input.

1. f(x) = x – 3 2. d(t) = 3t2 + 2 3. j(k) =

Find Function Values

If g(x) = x2 + 8x – 24, find each function value

1. g(6)

2. g(3)

3. g(4x)

4. g(5c + 4)

1. g(6) = 60

2. g(3)= 9

3. g(4x) = 16x2 + 32x – 24

4. g(5c + 4) = 25c2 + 80c + 24

Find more function values for d(t)= 2t2 + 3t - 91. d(2t)

2. d(-t)

3. d(x – c)

1. d(2t) = 8t2 + 6t – 9

2. d(-t) = 2t2 – 3t - 9

3. d(x – c) = 2x2 – 4xc + 2c2 + 3x – 3c - 9

EXIT TICKET - Sep 10th

1. Describe why the vertical line test determines if a graph is a function.

2. Represent in function notation a function for which the output is three times the input cubed.

3. The set of all inputs of a function is called the…4. The set of all outputs of a function is called the…5. For the function c(x) = 3x2 – 2x – 5, evaluate c(3x) and c(s+t)

UNIT 1

FUNCTIONS

1-1 September 14th

Function Introduction

SWBAT evaluate a piecewise-defined function

SWBAT graph a piecewise-defined function

A piece-wise defined function…Is a function defined using two or more equations for different intervals of the domain.

Such as…

Evaluate g(3), g(4), and g(5)

g(3) = -3

g(4) = 4

g(5) = 5

Evaluate g(x)

1. gEvaluate g(-4), g(-1), and g(2)

2.gEvaluate g(-7), g(0), and g(1)

g(-4) = 1g(-1) = 1g(2) = 4

g(-7) = -2g(0) = -4g(1) = 4

Graphing Piece-Wise Defined Functions

Open dots occur when endpoints are not included (< instead of

Closed dots occur when endpoints are included(

Notice the intervals of the domain of each equation

Graphing Practice

g

EXIT TICKET

Graph and Evaluate

Evaluate f(-2), f(0), and f(1)