Algebra II Review 4/1-4
1. Graph each of the following using the parent function as a guide. State the asymptote, the domain,
and the range of each function.
a. f(x) = 2x + 3
b. f(x) = 3x + 2
-2
-1
8
8
6
6
4
4
2
2
0
1
2
3
4
-8
-6
-4
-2
0
-2
-2
-4
-4
Does the function show growth or decay?
2. f(x) = 0.4x
3. f(x) = 1.2(2/5)x
x
6. f(x) = 5.1
7. f(x) = 0.3(1/4)x
4. f(x) = 7/8(1.1)x
8. f(x) = 21(9/2)x
2
4
5. f(x) = 50(1+ 0.04)x
9. f(x) = 30(1 – 0.04)x
10. Gina buys a car for $13,500. Its value will decrease by 15% per year. Write an exponential function
to model the value of the car. What will be the value of the car in 5 years? Graph the function on
the graphing calculator and use the graph to predict when the value of the car will be $3000.
11. John invests $1500 in an account which will increase by 4% per year. Write an exponential function
to model the value of the investment. What will be the value of the account after 10 years? Graph
the function on the graphing calculator and use the graph to predict when the value of the
investment will be $3000.
Write each exponential equation in logarithmic form.
12. 161/4 = 2
13. 16-0.5 = 1/4
14. 35 = 243
16. (1/3)-3 = 27
17. 91.5 = 27
18. 104 = 10,000
15. 90 = 1
19. 6-1 = 1/6
Write each logarithmic equation in exponential form.
20. log1/4 64 = -3
21. log81 1/3 = -1/4
22. log2 16 = 4
24. log0.6 0.36 = 2
25. log2 128 = 7
26. log8 64 = 2
23. log 10 = 1
27. log4 (1/16) = -2
28. Graph each of the following using the parent function as a guide. State the asymptote, the domain,
and the range of each function.
a. f(x) = 3 + log2 x
b. f(x) = log3 (x + 2)
8
8
6
6
4
4
2
2
-2
-1
0
-2
-4
1
2
3
4
-4
-3
-2
-1
0
-2
-4
1
2
Answers:
1. a.
b.
-2
-1
8
8
6
6
4
4
2
2
0
1
2
3
4
-4
-3
-2
-1
-2
-4
-4
3. Decay
7. Decay
4. Growth
8. Growth
10. A = 13500(1 – 0.15)t
11. A = 1500(1 + .04)t
b. y = 0
Domain: R
Range: y > 0
0
-2
2. Decay
6. Growth
a. y = 3
Domain: R
Range: y > 3
1
2
5. Growth
9. Decay
$5990
$2220
about 9 years
about 17.5 years
12. log16 2 = ¼
16. log1/3 27 = -3
13. log16 ¼ = -0.5
17. log9 27 = 1.5
14. log3 243 = 5
18. log 10,000 = 4
15. log9 1 = 0
19. log6 1/6 = -1
20. 64-3 = ¼
24. 0.62 = 0.36
21. 81-1/4 = 1/3
25. 27 = 128
22. 24 = 16
26. 82 = 64
23. 101 = 10
27. 4-2 = 1/16
28. a.
-2
b.
-1
8
4
6
3
4
2
2
1
0
1
2
3
4
-4
-3
-2
-1
0
-2
-1
-4
-2
a. x = 0
Domain: x > 0
Range: R
b. x = -2
Domain: x > -2
Range: R
1
2