Algebra 2 Unit 4 Chapter 6
Name ______________________
Review for Test
1.
Date ____________ Block _____
−3√𝑥 + 3
Graph equation
Domain _______________
Range ________________
2.
3
𝟐 √𝑥 + 3 − 1
Graph equation
Domain _______________
Range ________________
3.
Graph equation
4.
Graph equation
Domain _______________
Domain _______________
Range ________________
Range ________________
𝑓(𝑥) = 7𝑥 − 4 𝑎𝑛𝑑 𝑓 −1 (𝑥) =
5.Verify that the following are inverses:
1
7
𝑥+
They must both simplify to _____.
6.
7. Perform the following operations:
Given: 𝑓(𝑥) = 𝑥 + 5 𝑎𝑛𝑑 𝑔(𝑥) = 2𝑥
𝑓(𝑥) + 𝑔(𝑥)
𝑓(𝑥) ∙ 𝑔(𝑥)
1
𝑔(𝑥) − 𝑓(𝑥)
3
8. Given: 𝑓(𝑥) = 𝑥 5 𝑎𝑛𝑑 𝑔(𝑥) = 2𝑥 5
𝑓(𝑥) ∙ 𝑔(𝑥)
3
9. Given:
𝑓(𝑥)
𝑔(𝑥)
𝑓(𝑥)
𝑔(𝑥)
𝑔(𝑥)
𝑓(𝑥)
3
𝑓(𝑥) = 7𝑥 2 𝑎𝑛𝑑 𝑔(𝑥) = 4𝑥 2
𝑓(𝑥) − 𝑔(𝑥)
𝑔(𝑥) − 𝑓(𝑥)
4
7
10. Let 𝑓(𝑥) = −5𝑥 3 + 3 𝑎𝑛𝑑 𝑔(𝑥) = −2𝑥 3
11. 𝑓(𝑥) = 3𝑥 + 7 𝑎𝑛𝑑 𝑔(𝑥) + 2𝑥 − 5.
𝐹𝑖𝑛𝑑 𝑓(𝑔(𝑥)).
𝐹𝑖𝑛𝑑 𝑔(𝑓(−3))
12. 𝑔(𝑥) = −2𝑥 − 3 𝑎𝑛𝑑 ℎ(𝑥) = 2𝑥 2 + 2 𝐹𝑖𝑛𝑑 ℎ(𝑔(𝑥)).
13. Write the inverse of each:
𝑦 = −7𝑥 − 6
3
𝑦 = √𝑥 + 4 − 2
𝑦 = 3𝑥 2 − 4
3
7
5
5
𝑦=− 𝑥+
14. Write the equations with the following translations:
𝑦 = √𝑥
3
𝑦 = √𝑥
shift 3 units down and 4 units right __________________________
shift 6 units left and 4 units up, streched 2, and reflected ________________
15. 𝑟(𝑥) = −2𝑥 + 4 𝑎𝑛𝑑 ℎ(𝑥) = −3𝑥 2 + 3 𝑡𝑜 𝑓𝑖𝑛𝑑 ℎ(𝑟(−4))
16. Simplify
3
√64𝑥 3 𝑦
4𝑥 −3 𝑦
7
𝑥5
−7
𝑥5
4
4
𝑥5
𝑥5
17. Solve the equations, check for extraneous solutions. You will have to show all work for full credit on the
test even if you use your calculator
4
√𝑥 + 2 = √3𝑥 − 2
√2𝑥 − 2 = 1
5
(𝑥 − 5)3 − 73 = 170
(x = 32)
√4𝑥 + 1 = √𝑥 + 10
(x=3)
Study Guide #2 Chapter 6: Rational Exponents and Radical Functions
SOL: A2. T1, A2.T7
1.
9
Rewrite ( 8 15)3 using rational exponent notation.
2.
Rewrite
21 4
using radical notation.
Evaluate without a calculator. (questions 3-5)
3.
8
1
3
4.
6. Which expression has the greatest value? A.
25
27
3
3
2
5.
5
3
2
B.
5
C.
8.
x 6  34  181
3
64
2
3
D.
81
Solve. (questions 7 & 8)
7. x 5  48
Simplify. Assume all variables are positive: (questions 9-19)
9
9.
9
12.
4
10.
3
3
(12  8 )
5
5 5
11.
5
( 3 3  4 3)12
13
13
8  4 16
8
28 3
4
13.
14.
6
3
5
7
7
81
4
( 3 2)8
3
2
15.
x
3
16.
2
x  x5
17.
25 x16
3
4 x3 y 5  3 12 y 2
18.
20 x3 y 2
9 xz 3
19. Find a simplified expression for the perimeter of the rectangle.
20. Show that the hypotenuse of an isosceles right triangle with legs of length x is x 2 .
Let f ( x)  3 x
21.
1
3
 4x
1
2
and g ( x)  5 x
g ( x)  g ( x)
24.
2
3
3
22.
Domain:________
Range:__________
Let f ( x)  4 x
1
1
 4 x 2 . Perform the indicated operation. State the domain and range.
f ( x)  g ( x)
Domain:________
Range:__________
23.
g ( x)  f ( x)
Domain:_______
Range:________
1
and g ( x)  5 x 2 . Perform the indicated operation. State the domain and range.
f ( x)  f ( x)
Domain:________
Range:__________
25.
g ( x)
f ( x)
Domain:________
Range:__________
26.
g ( x)  f ( x)
Domain:_______
Range:________
Let f ( x)  3x  2 , g ( x)  3x 2 and h( x) 
27.
h( f (9))
28.
x2
. Evaluate the composition function.
5
29.
h(h( x))
f ( g ( x))
30.
g (h( x))
f ( x) 
2 x3  6
9
Find the inverse of the function or equation.
31.
2
y   x2
3
33. Verify that f ( x ) 
32.
2
f ( x)   x  2
5
33.
1
x  1 and g ( x)  3x 2 are inverses.
5
34. Graph f ( x)  x3  2 . Is the inverse a function? How do you know?
35. The euro is the unit of currency for the European Union. On a certain day, the number E of euros that could
Be obtained for D was given by the function E  .081419D . Find the inverse of the fuction. Then use the
Inverse to find the number of dollars that could be obtained for 250 euros on that day.
Describe the translation of each function compared to the parent. Then state the domain and range.
36.
1
x  4 ______________________________________________________________________________________
3
Domain:__________
37.
Range:__________
g ( x )  6 3 x __________________________________________________________________________________
Domain:__________
Range:__________
Describe the translation of each function compared to the parent. Then state the domain and range.
38.
y  4 x  5  1 _______________________________________________________________________________
Domain:__________
39.
Range:__________
h( x)  3 3 x  7  6 ____________________________________________________________________________
Domain:__________
Range:__________
Solve. (Check for extraneous solutions.)
2x 
40.
43.
3
2
0
3
x 3  2  4
41.
4 x  6  20
44.
(8 x)
4
3
 44  300
42.
45.
3
4x  5 
1
2
x  6  3x
46.
48.
3
44  2 x  x  10
47.
12 x  5  3 8 x  15  0
49.
x2 
3
x2
2
(2 x  3)  2  6 x  7