warm–up #2. warm–up #2 solutions y x │ –2 – 1 │ │ –1 – 1 │ │ 0 – 1 │ │ 1...
TRANSCRIPT
Warm–up #21. Graph 2. In a swimming pool where the water is 20 feet deep, the water pressure p at a point x feet above the bottom of the pool is p = 62.5(20 – x) pounds per square foot. Sketch the graph of this equation using appropriate restrictions on the variables.
Warm–up #2 Solutions1. Graph
y
x
│–2 – 1│
│–1 – 1│
│0 – 1│
│1 – 1│
│2 – 1│
–2
–1
0
1
2
3
2
1
0
1
x │y – 1│ y
Warm–up #2 Solutions2. p = 62.5(20 – x) p = 1250 – 62.5xp = – 62.5x + 1250(0, 1250) & (20, 0)p 0x 0
1250
20feet
pre
ssure
Homework LogMon
11/2
Lesson 3 – 2
Learning Objective: To find domain and range of a function
Hw: #303 Pg. 178 #1 – 43 odd
11/2/15 Lesson 3 – 2 Functions Day 1
Advanced Math/Trig
Learning Objective
To determine if relations are functions
To find domain of a function
To find range of a function
To find function values
To use function notations
VocabularyRelation – any set of ordered pairs
Domain – set of x – values
Range – set of y – values
Function – relation where x – values don’t repeat. Passes Vertical Line Test on a graph
f (x) “f of x” replaces/same as “y”
y = 2x – 4 f (x) = 2x – 4
Function1. Find domain & range and determine if the relation is a function. {(1, 2), (5, 4), (–3, 2)}
Domain: {–3, 1, 5}
Range: {2, 4}
Is a function because no x–value is repeated
Function2. Find domain & range and determine if the relation is a function. {(1, 2), (3, 4), (1, 5)}
Domain: {1, 3}
Range: {2, 4, 5}
Not a function because x = 1 twice with different y – values
Function3. Is x = y – 3 a function?
y = x + 3
Yes, passes the verticalline test
Domain: (
Range: (
Function4. Is y = a function?
–2 –1 0
1 2
1 0
2 3
x y
1
Function4. Is y = a function?
Yes, passes the verticalline test
Domain: (
Range: [ 0 1
–2 –1
1 2
1 0
2 3
x y
Finding Domain of an Equation
Domain: Look for any restrictions on x
(y must be real)
x under radical
x in denominator of a fraction
Finding Range of an Equation
Range: Look for any restrictions on y
(using known domain)
y = y 0
y 0
y = y 0
y = y 0
Draw a quick sketch if need
to or use graphing calculator
Find Domain & Range5. Domain All Real Numbers (can use any # for x))Range square of any number is 0 y 0 )
Find Domain & Range5. Domain All Real Numbers (can use any # for x))Range square of any number is 0 y 0 )
Find Domain & Range6. Domain x + 2 0 x –2 )Range will also come out 0 y 0 )
Find Domain & Range7. Domain x – 5 0 x 5)Range will also come out 0 , but it’s –! y 0
Find Domain & Range8. Domain x – 3 0 x 3 but can be everything
else! (3, )Range Could be anything but zero, will never
get y 0 (0, )
Find Domain & Range8. Domain x – 3 0 x 3 but can be everything
else! (3, )Range Could be anything but zero, will never
get y 0 (0, )
Find Domain & Range9. Graph it in Desmos!Vertex: (1, 5) Opens upDomain: Can plug in any x – values Range: Graph goes up from y = 5 [5, )
Find Domain & Range10. Graph it in Desmos!Vertex: (–2, 3) Opens downDomain: Can plug in any x – values Range: Graph goes down from y = 3 (, –3]
b. Find g (–2) = – (–2) = 4 + 2 = 6g (–2) = 6 (–2, 6)
a. Find f (–2) = 2(–2) = – 4f (–2) = – 4 (–2, –4)
Find Function Values11.
b. Find g (x + h) =– (x + h) =
a. Find g (–x) = – (–x) =
Function Notation12.
b. Find f (x + h) =(x + h) – 2 = 4x + 4h – 2
a. Find g (x + 1) = –2(x + 1) = =
Function Notation13.
Find f (x + h) – f (x) =(x + h) – 2 – (4x – 2) = 4x + 4h – 2 – 4x + 2 = 4h
Function Notation14.
Find g (x + h) – g (x) = –2(x + h) + 1 – ( + 1) = + 2x – 1 = 2xh +
Function Notation15. + 1
Find Domain & Range16. Domain – x +2 0 x 2
Range will also come out 0 y 0
Ticket Out the Door
Find f(x + h) – f(x)
Explain your process
Homework
#303 Pg. 178 #1 – 43 odd