Rocket City Math League Interschool Junior Test

Thursday 8amRoom 406 near the elevator

Algebra Quiz Thursday November 19th pages 208-235

Review Homework

Page 218/222

Page 222

#21. (0,0)2. (2,0)3. (8,5)4. (-6,-5)5. (0,1.5)6. (-2,1)

Graphs of Functions

Page 223

Vocab• Function Rule( 함수식 ) – an equation

that shows how variables are related.

• Table (or Table of Values) ( 표 )– shows the specific input and output or values of one variable based on the value of the other variable.

• example y=x+2x y-1 1

0 2

1 3

2 4

We Vocabulary

• Graph – a visual picture of a function, point or data

• Continuous data ( 연속데이터 )– There is data between points- a line, a ray or a line segment. If I ask for the weight of an object it could be any nonnegative number including decimals.

example-100.23 grams of meat (depending on the precision of the scale).• Discrete data ( 이산형데이터 ) – just points – the

values are not connected. If I ask for the number of desks, it could be any whole

number.

Graphing a function

• There are many ways to graph a function.

• One way is to make a table of values.

Making a Tablefor f(x) = -3x-2 page 224

x -3x-2 f(x)

Pick any values of x. Try and pick at least one negative, one positive and zero.For a line – use 3 points

-1

0

1

-3(-1)-2

-2-3(0)-2

-3(1)-2

1

-5

Now plot the points page 224

4

2

-2

-4

-6

-10 -5 5 10

(1,-5)

(-1,1)

(0,-2)

Practice – Page 225 # 1,2

Equation : f(x)=3x-2 x f(x)-3.0 -11.0-2.0 -8.0-1.0 -5.00 -2.01.0 1.02.0 4.03.0 7.0

225#2

x y-3.0 -3.5-2.0 -2.0-1.0 -0.50 1.01.0 2.52.0 4.03.0 5.54.0 7.0

Relations and Functions page 227

• A RELATION ( 관계 )is a set of ordered pairs.

• Domain( 정의역 ) is all the x (or first) values

• Range ( 치역 )is all the y (or second) values

• Mapping ( 연결하기 )matches each member

of the domain with a member of the range.

• List the domain, range and map the relation:

(1,2),(2,3),(3,3),(5,2)

(1,2),(2,3),(3,3),(5,2)

Domain = {1,2,3,5}Range = {2,3}

Function ( 함수 )

• A function is a relation that assigns exactly one output or range value for each input or domain value. Each x value corresponds with exactly one y value. Y-values can be repeated. X-values can not.

• (1,2), (2,2) is a function• (1,2), (1,3) is NOT a function.• If you map the relation and only one

arrow comes from a domain entry, the relation is a function.

• Ignore page 228 (Codomain)

Determine if the relation is a function

• (2,5),(3,-5),(4,5),(5,3)• When you map the relation, each

domain entry has only one arrow going to the range.

• 따라서 the relation is a function

Practice page 229 #1,2

#1 Not a FunctionDomain { 1,2,3,4 }Range { 3,5,6 }

#2 FunctionDomain { 0,1,2,3,4,5 }Range { 0,1,2,3,4,5 }

Determine if the relation is a function

• Another way to determine if a relation is a function is to use the vertical line test. If after you graph it, you can draw a vertical line on the graph and it only passes through one point, the relation is a function.

(page 229)한 x 값에 대해 두 가지 이상의 y 값이 존재하냐 안하냐를 판별하는 테스트

Since each vertical line crosses only one point the relation is a function.

x

y

The first graph is a function, the second is not.

x

y

x

y

Example

Use the vertical line test to identify graphs in which y is a function of x.

x

y

Function Notation ( 함수 표기법 )

page 232• Another way to write an equation instead

of y=2x+3 is function notation. • The output (y) is called f(x) pronounced

f of x• f(x)=2x+3• So when we choose 1 for x, we write

f(1)=2(1)+3 =5, so f(1) = 5. The coordinate is (1,5)

Making a table

x 2x+8 F(x)

-1 2(-1) + 8 6

0 8

2 12

10 28

Complete the table. The left column is the x-values (the domain). The middle column is to calculate the function. The right column is the output or the range.

The function is f(x) = 2x + 8

Writing Function Rule from Table

• Examine the table – see if it is simple - either constantly adding or multiplying.

y=3x y=x+2

x y

1 3

2 6

3 9

4 12

x y

1 3

2 4

3 5

4 6

Writing a function rule

x f(x)

0 5

1 8

2 11

4 17

336

112

Writing the Function Rule (cont.)

Homework

•Page 225 # 3•Page 226 # 4•Page 234 •Page 235 #9-12