Alg 2
Final Review – Part 2
Name__________
Please do this review in your notebook to prepare for the final.
1. Find the domain and range of each of the following relations. Indicate if the relation is a function.
(A) K={(9,1), (-2, 1), (0, 4)}
(B) P={(3,5), (5, 2), (3, -2)}
(C)
2. Given
f ( x)  2  6x , find each of the following: ( A) f (2); (B) f (5);  C  f (2k  3)
3. Given each of the following functions, find their inverse:
(B) f  x    x  2   1
( A) f  x   5x  3
f  x   3x  5 and
Given
4.
7.
2
g  x   2x2  4
2 f x
5.
f
g
 f  x

8. 
10.
g  x 
 f g  4
, find each of the following:
 f  g  x 
11.
6.
 g f  2 
9.
 f  g 5
3 g  6
Solve each of the following quadratics using the indicated method:
12. Factoring: 6 x 3  10 x  28 x 2
13. Completing the Square: x 2  4 x  13  0
14. Factoring: 8 x 4  50 x 2  0
15. Square Root Method: 9 x 2  25  0
16. Quadratic Formula: 3x 2  4 x  5  0
**Remember to find the discriminant to determine the nature of the solutions**
Solve the system using elimination or substitution:
y  x 2  4 x  19
17. 
y  5x  1
y   x 2  8 x  15
18. 
y  4 x  3
18. Indicate the changes to the parent function.
A) Parent:
B) Parent:
y x
y
New Function:
y  4 x  1  6
New Function:
y  3 x  7  2
3
x
19. Sketch a graph of each of the following.
Clearly indicate on the graph the key point.
Use a dotted line to represent a change in shape of the parent graph.
f  x   3 x  4  3
2
A)
B)
f  x   x  2  8
Graph each function using a table.
A) What is the y-intercept? B) Is this an exponential growth or decay?
20. y  (3) x
1
4
f  x    x  3  1
3
C)
C) Where is the asymptote?
x
21. y  2  
Write an equation and then solve.
22. A new car that sells for $52,000 depreciates 6% each year. Write a function that models the value of the
car. Find the value of the car after 4 yrs. Round to the nearest cent.
23. The mosquito population increases at a rate of 4.2% each year. There are 152,890 mosquitos this year.
Write a function that models the mosquito population. How many mosquitos will there be in 3 yrs? Round
to the nearest mosquito.
24. A radioactive material has a half-life of 12 years. Write the function for a 450 mg sample. Find the
amount of material remaining after 150 years. Round to the nearest hundredth.
25. Alycia deposited $400 in an account that compounded continuously over 6 yrs. If the annual interest is
2.25% find the amount in the account. Round to the nearest cent.
26. Kenny wants to save $8000 for college in five years. How much should be put into an account that
earns 5.2% annual interest compounded continuously? Round to the nearest cent.
Evaluate the logarithm by finding the same base.
13.
14. log 625 5
15. log
1
100
Solve for the exponent by finding the same base or logs.
16. 2 x 1  32
17. 9 x  27
18. 4 2x 
1
16
Using Logs, solve for the variable and round to the nearest ten-thousandth.
19. 5 x  12
20. 7 x 3  11
21. 6 5 x  4  11
22.  2 x  4  7  1
Use natural logarithms to solve the equation. Round to the nearest thousandth.
23. e x 1  11
24. e 3 x  7  15
25. 5
26. -
Solve the following problems and round nearest whole number.
27. Your account has accumulated $6,300 by compounding continuously. If your rate is 3.5% and you
invested $1000, find how many years did it take to save that money.
28.Suppose you invest $580 compounded continuously over 6 years. Find the rate that will make $3600.