1. No category

Name———————————————————————— Chapter
3
Date —————————————
Chapter Test A
For use after the chapter “Rational Exponents and Radical Functions”
Find the indicated real nth root(s) of a.
Answers
1. n 5 3, a 5 28
1.
2. n 5 4, a 5 256
2.
3. Evaluate 227
4/3
without using a calculator.
3}
​    22358 ​ 
using
4. Evaluate Ï
a calculator. Round the result to two
decimal places if appropriate.
3.
4.
Simplify the expression. Assume all variables are positive.
5.
32/3
5.​ }
   
​
321/3
6.
}
}
6. 8​Ï 8 ​ 2 4​Ï 18 ​ 
7. y 2 p y 3/4
8. x15 p x 20
7.
8.
9.
Let f (x) 5 2x 3 2 5 and g(x) 5 3x 2. Perform the indicated
operation and state the domain.
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
9. f(x) 1 g(x)
10.
g(x)
10.​ }  
​
f(x)
11.
11. f(g(x))
12. You are shopping at a nutritional supplement store for whey protein.
The original price of the protein is $39.99. You have a discount card
that gives 20% off the purchase price. You also have a $10 gift card
that can be applied to your purchase. Which discount should be
applied first to give you the best deal? State the lowest final price.
Use composition of functions to determine your answer.
12.
13.
Verify that f and g are inverse functions.
x25
13. f(x) 5 2x 1 5, g(x) 5 ​ }
   
​ 
2
14.
3}
14. f(x) 5 Ï
​    x ​,  g(x) 5 x 3
Find the inverse of the function.
15.
1
15. f(x) 5 ​ }  ​  x 4, x ≥ 0
16
16.
2x 1 5
16. f(x) 5 ​ }
   
​ 
3
Algebra 2
Assessment Book
35
Name———————————————————————— Date —————————————
Chapter Test A Chapter
continued
For use after the chapter “Rational Exponents and Radical Functions”
3
Graph the function. Then state the domain and range.
}
17. y 5 2​Ï x ​ 
18. y 5
y
3}
23​    x ​ 
Ï
17.
y
1
Answers
1
1
x
1
x
18.
}
19. y 5 2​Ï x 1 2 ​ 
22
19.
y
1
1
x
20.
1
3}
y
21.
22.
1
1 x
23.
24.
Solve the equation.
3}
21. 4 5 Ï
​   2x 2 8 ​ 
2/3
22. (x 2 2 1)
1256
}
23. x 1 2 5 ​Ï 28 2 x ​ 
}
}
24.​Ï 3x 1 5 ​ 
5Ï
​ 4x 2 2 ​ 
36
Algebra 2
Assessment Book
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
20. y 5 ​ }2 ​ ​ Ï x 1 3 ​ 
21
Name———————————————————————— Chapter
3
Date —————————————
Chapter Test B
For use after the chapter “Rational Exponents and Radical Functions”
Answers
1. Find the indicated real nth root(s) of a.
1.
n 5 5, a 5 232
Evaluate the expression without using a calculator.
3}
3}
2.​ Ï  729 ​ 
3.​ Ï  343 ​ 
5}
​    2748 ​ 
using
4. Evaluate Ï
a calculator. Round the result to two decimal
places if appropriate.
2.
3.
4.
5. In physics, transitional kinetic energy E (in Joules) is given by the
5.
1
equation E 5 }
​ 2 ​ mv 2, where m represents the mass (in kilograms), and
6.
v the velocity (in meters per second). Find the velocity of a thrown
7.
baseball at time of release whose mass is 0.148 kg, and whose
transitional kinetic energy is equal to 90.65 Joules.
8.
Simplify the expression. Assume all variables are positive.
9.
2721/3
6.​ }
  
​
2724/3
10.
}
}
7.​Ï 80 ​ 2 Ï
​ 245 ​ 
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
3}
8.​ Ï  2125x 3 ​ 
11.
4y 2.7
9.​ }
  
​
y 1.35
Let f (x) 5 x 2 2 4, and g(x) 5 2x 3. Perform the indicated
operation and state the domain.
10. f(x) 2 g(x)
12.
13.
11. g(x) p g(x)
12. g( f(x))
13. A rental car costs $35 for a 1-day rental, plus $.05 per mile. The total
cost (in dollars) is given by the equation C(m) 5 35 1 0.05m where
m represents the mileage. The car averages 32 miles per gallon,
and so the total mileage is given by the equation m(g) 5 32g. Find
C(m(g)), and find the total cost after using 8 gallons of gas.
14.
15.
Verify that f and g are inverse functions.
x14
14. f(x) 5 3x 2 4, g(x) 5 ​ }
   
​ 
3
Î
}
x
15. f(x) 5 2x 5, g(x) 5 ​ 5 ​ } ​ ​ 
2
Algebra 2
Assessment Book
37
Name———————————————————————— Date —————————————
Chapter Test B Chapter
continued
For use after the chapter “Rational Exponents and Radical Functions”
3
Find the inverse of the function.
Answers
3
17. g(x) 5 ​ } ​ x 3 1 4
2
16. f(x) 5 3x 8, x ≤ 0
16.
Graph the function. Then state the domain and range.
18.
3 3}
19. y 5 2​ } ​ ​ Ï  x ​ 
4
2 }
18. y 5​ } ​ ​Ï x ​ 
3
y
y
1
1
1
x
17.
1
x
19.
3 }
20. y 5 ​ } ​ ​Ï x 1 4 ​ 
21
5
20.
y
1 x
21.
1 3}
21. y 5 2​ } ​ ​ Ï  x 2 2 ​ 
12
2
y
1
22.
1
x
Solve the equation.
5}
22.​ Ï  4x 2 8 ​ 
52
1
23. 60 2 ​ }  ​ (x 1 75)3/2 5 10
20
}
24. x 1 1 5 ​Ï 19 2 x ​ 
}
}
25. 4​Ï x ​ 2 2 5 Ï
​ 5 2 x ​ 
38
Algebra 2
Assessment Book
23.
24.
25.
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
1
Name———————————————————————— Chapter Test C
Chapter
3
For use after the chapter “Rational Exponents and Radical Functions”
1. Find the indicated real nth root(s) of a.
Answers
n 5 4, a 5 81
1.
Evaluate the expression without using a calculator.
5}
3}
2.​ Ï  243 ​ 
3.​ Ï  2125 ​ 
3}
​    1228 ​ using
4. Evaluate Ï
a calculator. Round the result to two decimal
places if appropriate.
Simplify the expression. Assume all variables are positive.
1 
}
}
6. 3​Ï 28 ​ 2 Ï
​ 63 ​ 
Î
}
3.
4.
5.
7.
8.
32x 5
7.​ ​ }3  
​ ​ 
27x
1 1 
2.
6.
2
3631/6 3
5.​ }
​  1/12   
​  ​
9
22
2x 11/6 2 3
8.​ ​ }
​  4/3   
 
​  ​   ​
x
Let f(x) 5 x 3 2 x 2 and g(x) 5 3 2 x 2. Perform the indicated
operation and state the domain.
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Date —————————————
9.
10.
9. g(x) 2 f (x)
10. f(x) p g(x)
11.
11. g( f(x))
Find the inverse of the function.
12.
3
2x 1 3
12. f(x) 5 ​ }
   
​ 
7
13.
13. g(x) 5 x 4 1 5, x ≥ 0
14.
14. The formula for converting temperatures from degrees Kelvin K to
9
degrees Fahrenheit F is F 5 }
​ 5 ​ K 2 459.67. Find the inverse of this
15.
function, and find the equivalent temperature of 21218F in degrees
Kelvin.
Verify that f and g are inverse functions.
16.
2x 2 6
3x 1 6
15. f(x) 5 ​ }
   
​, g(x) 5 }
​  2   
​ 
3
}
1
16. f(x) 5 ​ } ​ x 2/3 2 5, g(x) 5 Ï
​
(4x 1 20)3 ​ 
4
Algebra 2
Assessment Book
39
Name———————————————————————— Chapter
3
Date —————————————
Chapter Test C continued
For use after the chapter “Rational Exponents and Radical Functions”
Graph the function. Then state the domain and range.
Answers
3
17. y 5 2​ } ​ ​Ï x ​ 
2
17.
2
18. y 5 2​ } ​ ​ Ï  x ​ 
3
}
3}
y
y
1
1
1
x
1
x
18.
}
19. y 5 22​Ï x 1 3 ​ 
11
19.
y
1
1
x
1 3}
20. y 5 2​ } ​ ​ Ï  x 2 1 ​ 
13
3
y
21.
22.
23.
1
1
x
Solve the equation.
3}
21.​ Ï  28x3 ​ 
5 16
22. (x 1 4)2/3 5 x
}
23.​Ï x 1 13 ​ 
5x11
}
}
24.​Ï 4x 1 5 ​ 
5Ï
​ 10x 2 1 ​ 
22
40
Algebra 2
Assessment Book
24.
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
20.
Answers for
Rational Exponents and Radical Functions
Quiz 1
y
4.
1
1. 4 2. }
​ 729   ​  3. 2625 4. 28 5. 1.90
; domain: all real numbers;
range: all real numbers
1
2
6. 22.76 7. 2.06 8. 27.21 9. 12
}
20 1 4​Ï17 ​ 
y
5.
; domain: all real numbers;
range: all real numbers
answers
2
10. 65 5 7776 11. 4x 4/5y 2/5 12. 1 13. ​ }
   ​ 
27x 6
}
14. 25x 4/5y 3 15. 16 1 4 1 Ï
​ 162 1 42 ​ 
;
x
Quiz 2
1. 8x3 2 2x; all real numbers 2. 2x 3 2 2x; all
real numbers 3. 15x 6 2 6x 4; all real numbers
5x 2 2 2
4. }
​ 
   
​ ; all real numbers except 0
3x 2
5. 135x 9 2 6x 3; all real numbers
2
2
6.
x
2
y
2
; domain: all real numbers;
range: all real numbers
x
3
6. 3(5x 3 2 2x) ; all real numbers
7. f(g(x)) 5 x, g( f(x)) 5 x
8. f(g(x)) 5 x, g( f (x)) 5 x
9. f(g(x)) 5 x, g( f (x)) 5 x
Î
}
10
8
1
10. f 21(x) 5 }
​ 3 ​ x 2 }
​ 3  ​ 11. f 21(x) 5 ​ 7 2​ }3 ​ x ​ 
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
}
12. f 21 (x) 5 Ï
​ x 1 9 ​ 
; x ≥ 29
13. C(g(d)) 5 0.05625d 1.24; $124.98; cost of
gasoline for 500 mi
5
7. 8 8. 4 9. 0 10. 8 11. }
​ 4 ​ 12. 28
13. 20.29 ft
Chapter Test A
1. 22 2. 64 3. 281 4. 213.31 5. 3
}
6. 4​Ï 2 ​ 
7. y 11/4
8. x 35
9. 2x 3 1 3x 2 2 5; all real numbers
Quiz 3
y
1.
; domain: all real numbers;
range: all real numbers
1
1
x
Î
}
3x 2
5
10. ​ }
   ​; all real numbers except ​ 3 }
​ 2 ​ ​ 
3
2x 2 5
11. 54x 6 2 5; all real numbers
12. 20% off discount; $21.99
13. f (g(x)) 5 x, g( f (x)) 5 x
; domain: x ≥ 0;
range: y ≥ 5
y
2.
14. f (g(x)) 5 x, g( f (x)) 5 x
4}
3x 2 5
15. f 21(x) 5 2​ Ï  x ​  16. f 21(x) 5 }
​  2   
​ 
1
1
3.
; domain: x ≥ 0; range: y ≥ 0
y
17.
1
x
1
x
; domain: x ≥ 4;
range: y ≥ 6
y
y
18.
2
; domain: all real numbers;
range: all real numbers
1
2
x
1
x
Algebra 2
Assessment Book
A5
continued
; domain: x ≥ 22;
range: y ≥ 22
y
1
answers
1
y
21.
x
; domain: all real numbers;
range: all real numbers
1
1
y
20.
; domain: all real numbers;
range: all real numbers
1
Chapter Test C
}
10. 2x 5 1 x 4 1 3x 3 2 3x 2; all real numbers
21. 36 22. 63 23. 3 24. 7
11. 2x 6 1 2x 5 2 x 4 1 3; all real numbers
Chapter Test B
Î
}
1. 22 2. 9 3. 7 4. 23.76 5. 35 m/s 6. 27
}
7. 23​Ï 5 ​  8. 25x 9. 4y 1.35
3
22. 10 23. 25 24. 3 25. 1
1. 63 2. 3 3. 25 4. 10.71 5. 11 6. 3​Ï 7 ​ 
}
4​Ï 6 ​ 
7. ​ }
  
​  x 8. 64x 3 9. 3 2 x 3; all real numbers
9
x
24
x
4}
7x 2 3
​  2   
​ ​  13. g21(x) 5 Ï
​   x 2 5 ​ 
12. f 21(x) 5 ​ 3 }
5
14. K 5 }
​ 9 ​ (F 1 459.67); 188.158K
2
10. x 1 x 2 4; all real numbers
15. f (g(x)) 5 x, g( f (x)) 5 x
11. x 6; all real numbers
12. 2x 6 1 12x 4 2 48x 2 1 64; all real numbers
13. C(m(g)) 5 35 1 1.6g; $47.80
16. f (g(x)) 5 x, g( f (x)) 5 x
14. f(g(x)) 5 x, g( f (x)) 5 x
1
1
15. f(g(x)) 5 x, g( f (x)) 5 x
Ï
}
; domain: x ≥ 0; range: y ≤ 0
y
17.
x
}
3 2x 2 8
8 x
16. f –1(x) = 2​    ​ } ​ ​  17. f –1(x) = ​    }
​  3   
​ ​  
3
Ï
y
18.
; domain: x ≥ 0; range: y ≥ 0
y
18.
1
1
1
x
y
19.
; domain: all real numbers;
range: all real numbers
1
2
; domain: all real numbers;
range: all real numbers
19.
; domain: x ≥ 24;
range: y ≥ 21
20.
y
1
1
; domain: x ≥ 23;
x range: y ≤ 1
x
y
20.
x
21
1
1 x
y
; domain: all real numbers;
range: all real numbers
1
1
x
21. 28 22. 4 23. 3 24. 5
A6
Algebra 2
Assessment Book
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
19.