Mathematics Vision Project Answer Key Math 2 Module 1
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Transcript of SECONDARY MATH II // MODULE 1 QUADRATIC SECONDARY MATH II // MODULE 1 QUADRATIC FUNCTIONS...
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SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.1
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
1.1
Need help? Visit www.rsgsupport.org
READY Topic: Distributive Property Simplify the following expressions
1. 3 2x + 7 2. −12 5x − 4
3. 5a −3a + 13 4. 9x 6x − 2
5. !" ! 12x + 18 6. !"
! 10a − 25b 7. !!"
!! 121x + 22
SET Topic: Recognizing Linear Exponential and Quadratic Functions In each set of 3 functions, one will be linear and one will be exponential. One of the three will be a new category of function. List the characteristics in each table that helped you to identify the linear and the exponential functions. What are some characteristics of the new function? Find an explicit and recursive equation for each. 8. Linear, exponential, or a new kind of function?
a.
Type and characteristics?
Explicit equation:
Recursive equation:
𝑥 𝑓(𝑥)
6 64
7 128
8 256
9 512
10 1024
b.
Type and characteristics?
Explicit equation:
Recursive equation:
𝑥 𝑓(𝑥)
6 36
7 49
8 64
9 81
10 100
c.
Type and characteristics?
Explicit equation:
Recursive equation:
𝑥 𝑓(𝑥)
6 11
7 13
8 15
9 17
10 19
READY, SET, GO! Name Period Date
Answer: 6x+21 Answer: -60x+48
Answer: -15a2+65a Answer: 54x2 – 18x
Answer: 8x2+12x Answer: 8a2 – 20ab Answer: -44x2 – 8x
Answer: Ratio of 2 between outputs, Exponential.
Answer: Goes by different amounts, new kind.
Answer: Difference of 2 between outputs, Linear.
Answer: 𝒇(𝒙) = 𝟐𝒙 Answer: 𝒇(𝒙) = 𝒙𝟐 Answer: 𝒇(𝒙) = 𝟐𝒙 − 𝟏
Answer: 𝒇(𝒙) = 𝒇(𝒙 − 𝟏) ∙ 𝟐 𝒇(𝟏) = 𝟐
Answer: 𝒇(𝒙) = 𝒇(𝒙 − 𝟏) + 𝟐𝒙 − 𝟏 𝒇(𝟔) = 𝟑𝟔
Answer: 𝒇(𝒙) = 𝒇(𝒙 − 𝟏) + 𝟐 𝒇(𝟔) = 𝟏𝟏
Answer: Different, not expected students can create yet.
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SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.1
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
1.1
Need help? Visit www.rsgsupport.org
9. Linear, exponential, or a new kind of function? d.
Type and characteristics?
Explicit equation:
Recursive equation:
𝑥 𝑓(𝑥)
-2 -17
-1 -12
0 -7
1 -2
2 3
e.
Type and characteristics?
Explicit equation:
Recursive equation:
𝑥 𝑓(𝑥)
-2 1/25
-1 1/5
0 1
1 5
2 25
f.
Type and characteristics?
Explicit equation:
Recursive equation:
𝑥 𝑓(𝑥)
-2 9
-1 6
0 5
1 6
2 9
10. Graph the functions from the tables in #8 and #9. Add any additional characteristics you notice from the graph. Place your axes so that you can show all 5 points. Identify your scale. Write your explicit equation above the graph. a. Equation:
b. Equation:
c. Equation:
d. Equation:
e. Equation:
f. Equation:
Answer: Difference of 5 between outputs, Linear.
Answer: Ratio of 5 between outputs, Exponential.
Answer: Different amounts being added, new kind.
Answer: 𝒇(𝒙) = 𝟓𝒙 − 𝟕 Answer: 𝒇(𝒙) = 𝟓𝒙 Answer: 𝒇(𝒙) = 𝒙𝟐 + 𝟓
Answer: 𝒇(𝒙) = 𝒇(𝒙 − 𝟏) + 𝟓 𝒇(𝟏) = −𝟐
Answer: 𝒇(𝒙) = 𝒇(𝒙 − 𝟏) ∙ 𝟓 𝒇(𝟏) = 𝟓
Answer: 𝒇(𝒙) = 𝒇(𝒙 − 𝟏) + 𝟐𝒙 − 𝟏 𝒇(𝟏) = 𝟔
Answer: Different, not expected students can create yet.
Answer: 𝒇(𝒙) = 𝟐𝒙 Answer: 𝒇(𝒙) = 𝒙𝟐 Answer: 𝒇(𝒙) = 𝟐𝒙 − 𝟏
Answer: 𝒇(𝒙) = 𝟓𝒙 − 𝟕 Answer: 𝒇(𝒙) = 𝟓𝒙 Answer: 𝒇(𝒙) = 𝒙𝟐 + 𝟓
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SECONDARY MATH II // MODULE 1
QUADRATIC FUNCTIONS – 1.1
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
1.1
Need help? Visit www.rsgsupport.org
GO Topic: Rates of Change Identify the rate of change in each of the representations below.
11.
12. 13.
x f(x)
25 65
26 68
27 71
28 74
14.
f 0 = 7; f n + 1 = f n + 5
15.
16.
Slope of 𝐴𝐵
A(-3, 12) B(-11, -16)
17. George is loading freight into an elevator. He notices that the weight limit for the elevator is 1000 lbs. He
knows that he weighs 210 lbs. He has loaded 15 boxes into the elevator. Each box weighs 50 lbs. Identify
the rate of change for this situation.
18.
Independent variable 4 5 6 7 8
Dependent variable 5 5.5 6 6.5 7
19.
𝑓 −4 = 24 𝑎𝑛𝑑 𝑓 6 = −36
4
3
2
1
–1
–2
–3
–4
–6 –4 –2 2 4 6
4
3
2
1
–1
–2
–3
–4
–6 –4 –2 2 4 6
4
3
2
1
–1
–2
–3
–4
–6 –4 –2 2 4 6
Answer: 4 Answer: -3
Answer: 3
Answer: 5
Answer: 𝟐 𝟓
Answer: 𝟕 𝟐 = 𝟑.𝟓
Answer: 50 lbs per box
Answer: .5
Answer: -6
Mathematics Vision Project Answer Key Math 2 Module 1
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