Chapter 7 – Roots, Radicals, and Function Operations 7.1
Answer Key
Defining nth Roots
Answers 1.
33 3
2.
5
3.
81
4.
25 4
5.
10
6.
625 64
7.
32
8.
4 27
9.
34 3 2
10. 2 x 3 3x 2 11. 2 xy 3 4 3x3 y 12. 2 xy 5
5 x3 y2
13. 100x 4 14.
3x z2
4
2x y3 z 2
15. 8 x 4 y 6 10 x
CK-‐12 Algebra II with Trigonometry Concepts
1
Chapter 7 – Roots, Radicals, and Function Operations 7.2
Answer Key
Rational Exponents and Roots
Answers 1. 451 5 ≈ 2.14 2. 1401 9 ≈ 1.73 3. 503 8 ≈ 4.34 5
4. 3 72 ≈ 1246.10 5. 3 952 ≈ 20.82 3
6. 4 125 ≈ 37.38 7.
16
8.
81
9.
32
10.
125
11.
243
12.
4
13.
4 9
14.
1 4
15.
8
CK-‐12 Algebra II with Trigonometry Concepts
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Chapter 7 – Roots, Radicals, and Function Operations 7.3
Answer Key
Applying the Laws of Exponents to Rational Exponents
Answers 1.
25a 7 5
2.
49b 2 3
3.
m2 9
4.
x1 2 y1 6
5.
2r 4 5 s 5 4t 4 9
6.
a 5 b8 3 3 2 15 14
7. 5
x
y6
8.
32 x 243 y 2
9.
3125d 5 4 35 2
10.
3 2a1 2
11. 18m 2 15 n −1 10 12.
9 x1 4 y 7 5 25
13. 25
a7
x⋅6 y
14. 15.
5
6
x 3y
CK-‐12 Algebra II with Trigonometry Concepts
3
Chapter 7 – Roots, Radicals, and Function Operations 7.4
Answer Key
Graphing Square Root Functions
Answers 1.nonreal answer 2.
1.59
3.
0
4.all real numbers greater than or equal to 4. 5.ans-0702-01
6.ans-0702-02
CK-‐12 Algebra II with Trigonometry Concepts
4
Chapter 7 – Roots, Radicals, and Function Operations
Answer Key
7.ans-0702-03
8.ans-0702-04
CK-‐12 Algebra II with Trigonometry Concepts
5
Chapter 7 – Roots, Radicals, and Function Operations
Answer Key
9.ans-0702-05
10.ans-0702-06
CK-‐12 Algebra II with Trigonometry Concepts
6
Chapter 7 – Roots, Radicals, and Function Operations
Answer Key
11.ans-0702-07
12.ans-0702-08
CK-‐12 Algebra II with Trigonometry Concepts
7
Chapter 7 – Roots, Radicals, and Function Operations
Answer Key
13.ans-0702-09
14.ans-0702-10
CK-‐12 Algebra II with Trigonometry Concepts
8
Chapter 7 – Roots, Radicals, and Function Operations
Answer Key
15.ans-0702-11
16.ans-0702-12
CK-‐12 Algebra II with Trigonometry Concepts
9
Chapter 7 – Roots, Radicals, and Function Operations 7.5
Answer Key
Graphing Cubed Root Functions
Answers 1.
3
2.
-5
3.
3.39
4.ans-0702-13
5.ans-0702-14
CK-‐12 Algebra II with Trigonometry Concepts
10
Chapter 7 – Roots, Radicals, and Function Operations
Answer Key
6.ans-0702-15
7.ans-0702-16
CK-‐12 Algebra II with Trigonometry Concepts
11
Chapter 7 – Roots, Radicals, and Function Operations
Answer Key
8.ans-0702-17
9.ans-0702-18
CK-‐12 Algebra II with Trigonometry Concepts
12
Chapter 7 – Roots, Radicals, and Function Operations
Answer Key
10.ans-0702-19
11.ans-0702-20
CK-‐12 Algebra II with Trigonometry Concepts
13
Chapter 7 – Roots, Radicals, and Function Operations
Answer Key
12.ans-0702-21
13.ans-0702-22
CK-‐12 Algebra II with Trigonometry Concepts
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Chapter 7 – Roots, Radicals, and Function Operations
Answer Key
14.ans-0702-23
15.ans-0702-24
CK-‐12 Algebra II with Trigonometry Concepts
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Chapter 7 – Roots, Radicals, and Function Operations 7.6
Answer Key
Extracting the Equation from a Graph
Answers 1. y = 2. y =
x+7 3
x−3
3. y = −2 x + 5 4. y = 2 3 x + 2 5. y = 3 x + 8 − 6 6. y = − 3 x + 2 + 1 7. y = −2 3 x − 1 + 4 8. y = − x + 5 + 7 9. y =
1 8− x +3 2
10. y = −3 x + 6 − 3 11. y = 2 3 x − 2 + 7 12. y = 5 x + 1 + 6 13. y = 5
3
x +1 +6
14. y = 5
3
x − 7 + 16
15.Answers will vary.
CK-‐12 Algebra II with Trigonometry Concepts
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Chapter 7 – Roots, Radicals, and Function Operations 7.7
Answer Key
Solving Simple Radical Equations
Answers 1.
no
2.
yes
3.
no
4.
x=3
5.
x=3
6.
x = -4
7.
x=7
8. x = 10 9. x = 61 10. x = 6 11. x = 37 12. x = 87 13. x = 120 14. x = 72 15. x = 390
CK-‐12 Algebra II with Trigonometry Concepts
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Chapter 7 – Roots, Radicals, and Function Operations 7.8
Answer Key
Solving Radical Equations with Variables on Both Sides
Answers 1.
x=7
2. x = 33 3.
x=3
4. x = 6, 10 5. x = 2, -5 6. x = 2, 3 7.
x=7
8. x = 5, 6 9.x = -2, 2, -1 10. x = 5 11.x = -7, 7 12. x = 5 13.no solution 14.x = 120.41, -31.16 15.x = 10.60, 1.84
CK-‐12 Algebra II with Trigonometry Concepts
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Chapter 7 – Roots, Radicals, and Function Operations 7.9
Answer Key
Solving Rational Exponent Equations
Answers 1.
no
2.
yes
3.
no
4.
x=9
5. x = 64 6.
x=5
7. x = 11 8. x = 0, 4 9.
x=5
10. x = 27 11. x = 32 12. x = 128 13. x = 100 14.x = 2401 15. x = 3, 1
CK-‐12 Algebra II with Trigonometry Concepts
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Chapter 7 – Roots, Radicals, and Function Operations 7.10
Answer Key
Function Operations
Answers 1. x 2 + 5 x + 6 2. 5 x + 1 − 3
x −5, x ≥ 5
x2 + 5 3. , x>5 3 x −5 4. 5 x3 + x 2 + 25 x + 5 5. 9 x − 40 , x ≥ 5 6. 5 x 2 + 26 7.
3x
8. 45 x − 31 , x ≥ 4 9.
5
x, x≠0
10. 25 , x > 0 11.
12.
26 x, x≥0 5
1 , x>0 x
13. 5x , x ≥ 0 14.
x 5
15.
25 , x≠0 x
16.
25 , x>0 x
CK-‐12 Algebra II with Trigonometry Concepts
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Chapter 7 – Roots, Radicals, and Function Operations 7.11
Answer Key
Inverse Functions
Answers 1.(3, 2), (8, -4), (9, -5), (1, 1); yes 2.(-6, 9), (-5, 8), (3, 7), (3, 4) 3. f −1 ( x) =
x+9 6
4. f −1 ( x) =
1 − 3x ,x ≠ 0 4x
5.
f −1 ( x) = x 2 − 7, x ≥ 0
6. f −1 ( x) =
x − 5, x ≥ 5
7. f −1 ( x) = 8.
3
x + 11
f −1 ( x) = x5 − 16
9.
yes
10.
no
11.
no
12.
yes
13. f −1 ( x) =
7 ,x ≠1 x −1
14. f −1 ( x) =
8x ,x ≠1 x −1
CK-‐12 Algebra II with Trigonometry Concepts
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Chapter 7 – Roots, Radicals, and Function Operations
Answer Key
212 − 32 180 9 = = 100 − 0 100 5 9 32 = (0) + b a). 5 b = 32 m=
15.
9 F = C + 32 5
b).
9 F = C + 32 5 9 F − 32 = C 5 5 ( F − 32 ) = C 9
9 ⎡5 ( F − 32 )⎤⎥ + 32 ⎢ 5 ⎣9 ⎦ F = F − 32 + 32 F=F or F=
c).
5⎛9 ⎞ C = ⎜ C + 32 − 32 ⎟ 9⎝5 ⎠ C =C
CK-‐12 Algebra II with Trigonometry Concepts
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