Multiple Choice. Identify the choice that best completes the statement or answers the question. 1. Evaluate the function at the indicated value of x. ...
Review Sheet - 3.1-3.3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Evaluate the function at the indicated value of
3. Use a graphing utility to construct a table of
values for the function. Round your answer to two decimal places.
x . Round your result to three decimal places.
Function f (x ) 0.5 x a. b. c. d. e.
Value x 1.7
f (x ) 6 x
0.308 1.7 0.308 0.5 1.7
a.
b.
2. Match the graph with its exponential function. c.
d.
e.
x
2
1
0
1
2
f (x )
36
6
1
0.17
0.03
x
2
1
0
1
2
f (x )
36
6
1
0.17
0.03
x
2
1
0
1
2
f (x )
36
6
1
0.17
0.03
x
2
1
0
1
2
f (x )
36
6
1
0.17
0.03
x
2
1
0
1
2
f (x )
36
6
1
0.17
0.03
4. Use the graph of f to determine the
transformation that yields the graph of g . a. b. c. d. e.
f (x ) 3 x , g (x ) 3 x 8
x
y 2 3 y 2 x 3 y 2x 3 y 2x 3 y 2 x 3
a. b. c. d. e.
Shift the graph of f eight units to the left. Shift the graph of f eight units upward. Shift the graph of f eight units to the right. Shift the graph of f eight units downward. Both the graphs f and g are same.
5. Select the graph of the exponential function.
f (x ) 5 x 2 3
1
Name: ________________________
ID: A
a.
d.
b.
e.
c.
6. Use the One-to-One Property to solve the
equation for x . 4 x 1 1024 a. b. c. d. e.
2
x x x x x
8 4 7 5 6
Name: ________________________
ID: A
7. Use the One-to-One Property to solve the
11. Write the logarithmic equation in exponential
equation for x .
form.
ÊÁ 1 ˆ˜ x ÁÁÁ ˜˜˜ ÁÁÁ 2 ˜˜˜ 16 Ë ¯
log32 16
a. b. c. d. e.
x x x x x
4
5 4 4 5 6
a.
32 4
b.
32
c.
16
4
4
8. Evaluate the function f(x) 1.3 at x 3.6 . x
d.
Round to 3 decimal places. a. 1.690 b. 2.572 c. 5.287 d. 20.055 e. 4.680
32 4
e.
32
5
5
4 5
16 1 16
5
32
5
16 1 16
5
12. Write the exponential equation in logarithmic
form.
9. Use the One-to-One Property to solve the
4 2
following equation for x.
1 16
2 128 3x
a. b. c. d. e.
7 3 3 7 128 3 2 64 3
log16
b.
log4
c. d. e.
1 4 1
2
2 16 log4 16 2 1 log4 2 16 log4 16 2
13. Evaluate f (x ) logx at the indicated value of
10. Write the logarithmic equation in exponential
form.
x. Round your result to three decimal places.
log7 343 3 a. b. c. d. e.
a.
x 12.5 a. b. c. d. e.
7 343 2 7 3 77 7 3 343 7 3 14 343 7 2
3
–1.097 1.097 0.912 0.08 –0.912
Name: ________________________
ID: A
14. Evaluate the function at the indicated value of
17. Use the properties of logarithms to simplify the
x 32 .
expression.
f (x ) log2 x a. b. c. d. e.
9
0
log 9 24
1
a. b.
5
c.
1
d.
5 5 5
e.
15. Evaluate the function at the indicated value of
f (x ) log(x 4)
f (x ) log3 x
a.
b. c. d. e.
1 3
1
3 3 0 3
16. Evaluate the function at the indicated value of
x b 8 . g (x ) logb x b. a. b. c. d. e.
24
18. Select the graph of the function.
x 1.
a.
24 0 1 24 24 1
8 0 1 8 8 1 8
4
Name: ________________________
ID: A 19. Use the One-to-One Property to solve the
c.
equation for x. log2 (x 4 ) log2 20 a. b. c. d. e.
19 17 18 16 20
20. Use the One-to-One Property to solve the
equation for x. log2 (8x 2) log2 14
d.
a. b. c. d. e.
8 1 6 3 2 1 14 1 8
21. Rewrite the logarithm as a ratio of common
logarithms. e.
log5 17 a. b. c. d. e.
5
log5 log17 17 log 5 log17 log5 5 log 17 None of these
Name: ________________________
ID: A
22. Rewrite the logarithm as a ratio of common
25. Use the properties of logarithms to expand the
logarithms.
expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
log3.1 x a. b. c. d. e.
log 3.1
log7
log x log x
a. b.
log 3.1 x log 3.1 log3.1x None of these
c. d. e.
23. Find the exact value of the logarithmic
expression without using a calculator.
2
2 3
y z
2 log7 x 2 log7 y 3 log7 z 2 log7 x 2 log7 y 3 log7 z 2 log7 x
2 log7 y 3 log7 z 2 log7 x 2 log7 y 3 log7 z 2 log7 x 2 log7 y 3 log7 z
C PTS: 1 REF: 3.1.7 C PTS: 1 REF: 3.1.14 E PTS: 1 REF: 3.1.19a B PTS: 1 REF: 3.1.23 A PTS: 1 REF: 3.1.31 B PTS: 1 REF: 3.1.51 B PTS: 1 REF: 3.1.53 B PTS: 1 REF: 3.1.7 OBJ: Raise number to a non-integer power A PTS: 1 REF: 3.1.52 Solve exponential equations using one-on-one property C PTS: 1 REF: 3.2.8 D PTS: 1 REF: 3.2.11 D PTS: 1 REF: 3.2.19 B PTS: 1 REF: 3.2.31 E PTS: 1 REF: 3.2.23 D PTS: 1 REF: 3.2.25 D PTS: 1 REF: 3.2.28 A PTS: 1 REF: 3.2.36 B PTS: 1 REF: 3.2.79 D PTS: 1 REF: 3.2.85 C PTS: 1 REF: 3.2.88 C PTS: 1 REF: 3.3.7a B PTS: 1 REF: 3.3.13a A PTS: 1 REF: 3.3.29 C PTS: 1 REF: 3.3.46 D PTS: 1 REF: 3.3.63 A PTS: 1 REF: 3.3.84 A PTS: 1 REF: 3.3.15 D PTS: 1 REF: 3.3.24 C PTS: 1 REF: 3.3.32 Evaluate logarithmic function using properties of logarithms C PTS: 1 REF: 3.3.26 OBJ: Simplify logarithmic functions A PTS: 1 REF: 3.3.43 Evaluate logarithmic function using properties of logarithms B PTS: 1 REF: 3.3.71 Condense logarithmic function using the properties of logs