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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