September 27 th

September 27th

Please Complete Warm Up

1. Solve and graph -10 < 2x – 5 ≥ 12

2. Solve for L: m=2∏²-2∏L

Warm-Up

Monday, September 30th

Functions vs Relations

Vocabulary•Coordinate Plane: Graph formed by the intersection of 2 number lines (axes)

•Origin: The point of intersection; (0,0)•X-axis: Horizontal Number Line•Y-axis: Vertical Number Line•Ordered Pair: Points on a graph (x-coordinate, y-coordinate)

Quadrants

Do you Remember How to Graph?!?!?!?

•X coordinate: Tells me how many units to move left of right

Negative: left Positive: right•Y Coordinate: Tells

me how many units to move up or down

Negative: downPositive: up

GraphA: (3,5) B: (-2, 4)

C: (3,-6)

1. EQuadrant ll

2. Fno quadrant (y-axis)

3. GQuadrant l

4. HQuadrant lll

•E•F

•H

•Gx

y

Name that Quadrant!

What is a Function? • It’s like a machine! You INPUT a number to

get an OUTPUT• Input: The value substituted for x•Output: The value generated to get y

y = 10x + 5Output Input

Let’s think About it……

Y = 3x

Input

Out put

Input: 5 Output:____Input: -2Output:___Input: 6 Output:____

An engraver charges a setup fee of $10 plus $2 for every word engraved. Write a rule for the engraver’s fee. Write ordered pairs for

the engraver’s fee when there are 5, 10, 15, and 20 words engraved.

Let y represent the engraver’s fee and x represent the number of words engraved.

Engraver’s fee is $10 plus $2 for each word

y = 10 + 2 · x

y = 10 + 2x

Real World Application

Number ofWordsEngraved

Rule Charges Ordered Pair

x (input) y = 10 + 2x y (output) (x, y)y = 10 + 2(5)5 20 (5, 20)

y = 10 + 2(10)10 30 (10, 30)

y = 10 + 2(15)15 40 (15, 40)

y = 10 + 2(20)20 50 (20, 50)

Organizing it All

Relation•Any set of input that has an output•Input and output values are ordered

Function•A relation where EACH input has exactly ONE output

•Each element from the domain is paired with one and only one element from the range

•Different input values can have the same output value.

Domain•x – coordinates•Independent variable•Input

Range•y – coordinates•Dependent variable•Output

How can I remember

Domain and Range?

NOTICEX comes before Y

&D (Domain) comes before R

(Range)X’s=DomainY’s= Range

How do I know it’s a function?

•Look at the input and output table – Each input must have exactly one output.•Look at the Graph – The Vertical Line test: NO vertical line can pass through two or more points on the graph

Vertical Line Test

Vertical Line Test:1. 2. 3.

Example 1:{(3, 2), (4, 3), (5, 4), (6, 5)}

function

Example 2:

function

Example 3:

relation

Example 4: ( x, y) = (student’s name, shirt color)

function

Example 5: Red Graph

relation

Function or Relation?

relation

Function Notation

Function form of an equation• A way to name a function

• f(x) is a fancy way of writing “y” in an equation.

• Pronounced “f of x”

Evaluating Functions

Evaluating a functionf(x) = 2x – 3 when x = -2

f(-2) = - 4 – 3 f(-2) = - 7

Tell me what you get when x is -2.

f(-2) = 2(-2) – 3

Evaluating a functionf(x) = x2 – 2x + 3 find f(-3)

f(-3) = 9 + 6 + 3f(-3) = 18

Tell me what you get when x is -3.

f(-3) = (-3)2 – 2(-3) + 3

Domain and Range

• Only list repeats once• Put in order from

least to greatest

What are the Domain and Range?

x 1 2 3 4 5 6y 1 3 6 10 15 21

Domain: Range:

{1, 2, 3, 4, 5, 6}{1, 3, 6, 10, 15,

21}

What are the Domain and Range?

Domain:

Range:

{0, 1, 2, 3, 4}

{1, 2, 4, 8, 16}

15. What are the Domain and Range?

Domain:

Range:

x ≥ -1

All Real Numbers

Homework/Classwork

Function Practice

Worksheet