Unit 3 · 2021. 7. 3. · Unit 3 Summer. Monday July 19, 2021 Activator +X +Y-X-Y Where is (3, 5)?...
Transcript of Unit 3 · 2021. 7. 3. · Unit 3 Summer. Monday July 19, 2021 Activator +X +Y-X-Y Where is (3, 5)?...
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Algebra
Unit 3
Summer
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Monday July 19, 2021 Activator
+X
+Y
-X
-Y
Where is (3, 5)? +3 right and +5 up
What does the 3 mean? Right
What does the 5 mean? Up
Is x the number line? Yes
New Seats
Page #3 Lesson 3.1
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Today’s Objective
Students will be able to graph lots of points in function notation.
Lesson 3.1
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Today’s New Vocab (1 of 4)Graph and connect the points in the following sequence.(-2,1) (2left, 1up)(2,-3) (2right, 3down)(2, 2) (2right, 2up)(-2,-3) (2left, 3down)(4, 0) (4right, 0up)(-2,1) (2left, 1up)
https://www.youtube.com/watch?v=r16I6LB2YbQ 0:30-2:30 and 4:15-6:15
A
C
BD
E
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Today’s New Vocab (2 of 4)Write the points in function notation.
f(0) =
G(3) =
H(6)=
5
3
1
(0, 5)
(3, 3)
(6, 1)
G
H
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Today’s New Vocab (3 of 4)
F(7) = -5
Write the function as a point.Graph the point.
(7, -5)
B(-4) = 6 (-4, 6)What point is this? F
What point is this? B
Right
Left
Down
UP
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Today’s New Vocab (4 of 4)
G(x) = -2x F(x) = x - 7 What is G(3) and F(4)?
G(3) = -2(3) G(3) = -6 (3, -6)
F(4) = (4) - 7 F(4) = -3
(4, -3)The point is...
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Group Work Questions
#1#2#3#4#5
#6#7#8#9#10
13, 3, 4, 10
17, 7, 8, 12
16, 5, 6, 11
13, 3, 4, 10
13, 3, 4, 10
13, 3, 4, 1016, 5, 6, 11
16, 5, 6, 11
17, 7, 8, 12
17, 7, 8, 12
Page #1 Lesson 3.1
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.
Monday July 19, 2021 Work PeriodGraph the points and write the functions.
(x, y)(-4, 4)(-2, 2)(0, 0)(2, -2)
X
y
F(-4) = 4
G(-2) = 2
H(0) = 0J(2) = -2
y = -x
Page #4 Lesson 3.1
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Monday July 19, 2021 Exit Ticket
.
Graph the table and write the functions.
X Y
-3 -6
-2 -4
1 2
2 4
X
y
F(-3) = -6G(-2) = -4H(1) = 2
J(2) = 4
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Make a table for this function.
X(input) f(x) (output)
-1 10
0 3
3 -6
4 -5
5 -2
Tuesday July 20, 2021 Activator
Right and Left Up and Down
Page #7Lesson 3.2
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Today’s Objective
Students will be able to determine if problems are functions.
Lesson 3.2
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Today’s New Vocab (1 of 4)Can the calculator make a table for you?
f(x) = 3x X Y
-1 -3
0 0
1 3
2 6
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Today’s New Vocab (2 of 4)
x (input) f(x) = 3x f(x) or y
f(-1) f(-1) = 3( -1 ) -3f(0) f(0) = 3( 0 ) 0f(1) f(1) = 3( 1 ) 3f(2) f(2) = 3( 2 ) 6
f(x) = 3x is a line on a graph.
If every point is f, then the line is called f.
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Today’s New Vocab (3 of 4)
X f(x) or y
-2 -6
-1 -3
0 0
1 3
2 6
f(x)= 3xMake a table and graph
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Is this a point or line at F(-4)? a pointF(x) = 3x F(-4) = -12
F(-4) = 3(-4) F(-4) = -12
F(x) is a line called F or F(x).
F(-4) is a point called F
(-4, -12)
Today’s New Vocab (4 of 4)
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Group Work Q’s Skip 2C,3A,3B
#1#2#3#4#5
#6#7#8#9#10
5BC,7BC, 1AB,2D
5DE,7DE,1AB,2D
5CD,7FG, 1AB,2D
5BC,7BC, 1AB,2D
5BC,7BC, 1AB,2D
5BC,7BC,1AB,2D5DE,7DE,1AB,2D
5DE,7DE,1AB,2D
5BC,7BC, 1AB,2D
5BC,7BC, 1AB,2D
Page #6Lesson 3.2
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Tuesday July 20, 2021 Work Period
.
f(x) = 2x g(x) = x + 2
What is f(3) + g(3) ? 6 + 5 is 11
What is f(3)(g(3)) ? 6(5) is 30
What is f(3) - g(3) ? 6 – 5 is 1
f(3) = 2(3) g(3) = (3) + 2
f(3) = ___ g(3) = ____ 6 5
Evaluate when g(3) and f(3). Page #8Lesson 3.2
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Tuesday July 20, 2021 Exit Ticket
.
Make a table from the graph.
A
B
C
D
X f(x)
0 3
2 2
4 1
6 0What is f(4)? 1
What is f(0)? 3
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Wednesday July 21, 2021 Activator Enter the function.Make a table. g(x) = x - 7
X G(x)
0 -7
1 -6
2 -5
3 -4
4 -3
5 -2
Page #11Lesson 3.3
Describe this line. Subtract 7
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Today’s Objective
Students will be able graph a function and determine if it is a function.
Lesson 3.3
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Today’s New Vocab (1 of 4)
X G(x)
0 -7
1 -6
2 -5
3 -4
4 -3
g(x) = x−𝟕Graph the function.
What is g(1)? -6
What is this point?
(1,-6)
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Today’s New Vocab (2 of 4)Evaluate the function for g(2) and g(4)
g(x) = x - 7
g(2) = (2) - 7
g(2) = 2 - 7 g(2) = -5
g(x) = x - 7
g(4) = (4) - 7
g(4) = 4 - 7g(4) = -3
What number was next to 4 on the table? -3
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Today’s New Vocab (3 of 4)What is a function? A function is an equationwhich gives a unique outputfor all inputs. Does something.
Is f(x) = x – 7 a function? Yes
X (input) Y (output)
0 -7
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Today’s New Vocab (4 of 4)This graph is f(x) = 𝑥2
What is f(-2)? 4
What is f(-1)? 1
What is f(0)? 0
Write the point. (-2,4)
Write the point. (-1,1)
Write the point. (0,0)
A
B
C
D
E
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Group Work Questions
#1#2#3#4#5
#6#7#8#9#10
1,3B,7AC,5D
1,3D,7AC,5C
1,3C,7BD,5B
1,3B,7BD,5D
1,3C,7AC,5B
1,3B,7AC,5D
1,3D,7BD,5C
1,3C,7BD,5B
1,3D,7AC,5C1,3B,7BD,5D
Page #9Lesson 3.3
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Wednesday July 21, 2021 WP
.
Is this diagram a function? NoWhy? x=2 has two y-values.
Page #12Lesson 3.3
X Y
2 20
2 40
3 30
4 40
Repeat x = 2
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Wednesday July 21, 2021 Exit Ticket
.
Translate the function into points, a table, and a graph.
f(-2) = 0f(-1) = 1
f(0) = 2
f(-3) = -1 (-3,-1) (-2,0) (-1,1) (0, 2)
X f(x)
-3 -1
-2 0
-1 1
0 2
f(x) = x+2
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Thursday July 22, 2021 Activator
What is the maximum(or top) of the parabola
(or curved line) f(x)?State the point. ( 2, 1 )
What is f(4)? -3
B
A C
Page #15Lesson 3.4
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Today’s Objective
Students will be able to determine the maximum and
minimum of a function.
Lesson 3.4
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Today’s New Vocab (1 of 4)Make a table for the function f(x) = 𝒙𝟐 − 𝟒
Where is the exponent button?
X Y
-3 5
-2 0
0 -4
2 0
3 5
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Today’s New Vocab (2 of 4)
X (Input) f(x) = 𝒙𝟐 − 𝟒 Y (output)
-3 (−𝟑)𝟐−𝟒 5
0 (𝟎)𝟐−𝟒 -4
3 (𝟑)𝟐−𝟒 5
What is f(-3)? 5 What is f(0)? -4What is f(3)? 5
How is the table calculated?
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Today’s New Vocab (3 of 4)
X Y
-3 5
-2 0
0 -4
2 0
3 5
f(x)= 𝒙𝟐 − 𝟒Graph the function.
Where is the minimum or
(bottom)?
(0,-4)
Smallest y-value
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Today’s New Vocab (4 of 4)Is f(x) = 𝒙𝟐 − 𝟒 a function? YES
Why?
Every x-value has exactly one answer when you substitute.
What is f(-5)?f(-5) = (−5)2−4
f(-5) = +25 −4
f(-5) = 21For example,
f(-5) = (-5)(-5) −4
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Group Work Questions
#1#2#3#4#5
#6#7#8#9#10
1A, 3A, 3B
4A, 4B , 4C
1B, 2A, 2B
1A, 3A, 3B
1B, 2A, 2B
1A, 3A, 3B
4A, 4B , 4C
1B, 2A, 2B
4A, 4B , 4C1A, 2A, 2B
Page #13Lesson 3.4
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Thursday July 22, 2021 Work Period
.
X G(x)
0 -6
1 -4
2 -2
3 0
Make a table for the function G(x) = 2x - 6
For what x-value does G(x) = 0 ? x = 3
What is G(3)?
G(3) = 6 - 6G(3) = 2(3) - 6
G(3) = 0 Page #16Lesson 3.4
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C
A
Thursday July 22, 2021 Exit Ticket
.
For what value of
x does f(x) = 2? (-2,2)
For what value of
x does G(x) = 0? (3,0)
X
X
B
For what x-value does f(x) = G(x)? (1,-4)
X Intersection (solution)
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![Page 43: Unit 3 · 2021. 7. 3. · Unit 3 Summer. Monday July 19, 2021 Activator +X +Y-X-Y Where is (3, 5)? +3 right and +5 up What does the 3 mean? Right What does the 5 mean? Up Is x the](https://reader036.fdocuments.net/reader036/viewer/2022071607/6144d56234130627ed509a45/html5/thumbnails/43.jpg)
Test 3 InfoFriday July 23, 2021
#9-10 are worth double points.No work needed on #6.All other questions must have work.
![Page 44: Unit 3 · 2021. 7. 3. · Unit 3 Summer. Monday July 19, 2021 Activator +X +Y-X-Y Where is (3, 5)? +3 right and +5 up What does the 3 mean? Right What does the 5 mean? Up Is x the](https://reader036.fdocuments.net/reader036/viewer/2022071607/6144d56234130627ed509a45/html5/thumbnails/44.jpg)
Test 3 InfoMonday July 26, 2021
#9-10 are worth double points.No work needed on #6.All other questions must have work.