Composition Book Review
Chapter 7: Powers, Roots and Radicals
Chapter 8: Exponential and Logarithmic Functions
Simplify each expression. Assume that all the variables are positive.
1.
5.
 256 
7
3
2  2 
2
Let f ( x)  4 x
9.
4
3
1
2
2
2.

6.
 x 43 y5

 16 z 12

4
3
27

2




1
2
3.
32
7.
 3 12
 1
 12 2

4
5




4.
3
2
8.
8 x 6 y 2 z  x 3 27 x 3 y 2 z
 e3 x 


 2e 
2
and g ( x)  x  3 . Perform the given operation and state the domain.
f ( x)  g ( x)
10.
f ( g ( x))
11.
g ( x)
f ( x)
State whether the following statements are always true. If they are false, give an example.
12.
14.
f ( x)  g ( x)  g ( x)  f ( x)
13.
f ( g ( x))  g ( f ( x))
Verify that f ( x ) and g ( x ) are inverse functions.
f ( x)  x  4, g ( x)  x 2  4, x  0
15.
Find the inverse function of
f ( x)  2 x 3  5 .
Sketch the graph of the function. State the domain and range and describe the transformations of each from their
parent function.
16.
f ( x)   3 x  1  2
17.
f ( x)  2 x  3  1
Solve each equation, if possible.
18.
3
1
 3x  1 4  3  1
2
2x  3  1  x  1
19.
Sketch the graph of the function. State the domain and range and describe the transformations of each from their
parent function.
20.


f ( x)  3 2 x 1  4
21.
 
f ( x)  2 3 x  1
22.
f ( x)   log  x  2   1
Evaluate each expression.
23.
log 2
1
32
24.
log16 8
25.
log 6 1
Expand each expression.

2

3
26.
log 3xyz
28.
Condense the expression:
27.
log 2
 xy 
4
z2
1
log  x  5   2 log x  log y
2
Solve each equation. Round the result to three decimal places if necessary.
29.
32.
1
25 x 1   
5
x 3
30.
2.3x  48
31.
log  x  2  log  x  3  log  x  29 
Stereo System. You purchase a stereo system for $830. After a 3-month trial period, the value of the
stereo system decreases 13% each year.
a. Write an exponential decay model for the value of the stereo system in terms of the number of years
since the purchase.
b. What was the value of the system after 1 year?
33.
Phoebe Small is out driving in her Rocket Ship. She fills up with fuel at the Scorpion Gulch Rocket Fuel
Station, and takes off. When she starts the last stage of her rocket, she is going 4200 miles per hour.
Ten seconds later she is going 6850 miles per hour. While the last stage is running, you may assume
Phoebe’s speed increases exponentially with time.
a.
b.
c.
d.
Find the particular equation expressing the speed in terms of time.
In order to go into orbit, Phoebe must be going 17,500 mph. She took in enough fuel to last for 30
seconds. Will she reach orbit? Explain.
What is the minimum length of time the last stage could run and still get Phoebe into orbit?
How long would the last stage have to run to get Phoebe going 25,000 mph so that she could
cast off to the moon?
Name__________________________________
Composition Book Score Sheet
Chapter 7 and Chapter 8
NO YES ______ (4) Completed on time
NO YES ______ (1) Problems copied
NO YES _______ (3) All work shown
NO YES _______ (2) Corrections made
TOTAL ________ (10)
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