Algebra 2H B
Final Exam Review #4
Name:_______________________________________
Solve each equation. Be sure to check for extraneous solutions.
4√𝑥 + 7 − 9 = 15
1.
2.
√𝑥 + 1 = 𝑥 − 5
If 𝒇(𝒙) = 𝟕𝒙 − 𝟖 and 𝒈(𝒙) = 𝟒𝒙 + 𝟖, find the following:
3.
𝑓(𝑥) + 𝑔(𝑥)
4.
𝑓(𝑥) − 𝑔(𝑥
5.
( f g )(7)
6.
( g f )(7)
If 𝒇(𝒙) = 𝒙𝟐 − 𝟖𝒙 + 𝟏 and 𝒈(𝒙) = −𝟑𝒙, find the following:
7.
𝑓(𝑥) + 𝑔(𝑥)
8.
𝑓(𝑥) − 𝑔(𝑥
9.
( f g )(7)
10.
( g f )(7)
Find the inverse of each relation.
x2  3
y
2
11.
12. f ( x ) 
1 3
x
3
Graph each equation.
y  x 1
13.




𝑦 = 2𝑥
14.

y
y








y  x 3
15.
y







x








x




















x
𝑦 = 4𝑥
16.




𝑦 = 𝑙𝑜𝑔2 𝑥
17.

y
𝑦 = 𝑙𝑜𝑔4 𝑥
18.
y















x








x

















Write each expression as a single logarithm.
log5 x  5log5 w  3log5 y
19.
y

20.
4log12 c  log12 b  3log12 a
22.
𝑙𝑜𝑔2 3𝑥
24.
𝑙𝑜𝑔16 32


Expand each logarithm.
21.
𝑥
𝑙𝑜𝑔4 7
Use the change of base formula to evaluate each logarithm.
23.
𝑙𝑜𝑔8 45
25.
Suppose you invest $4000 into an account with an interest rate of 5.5% compounded continuously. How much
money will you have at the end of 15 years?
26.
Suppose you invest $2500 into an account with an interest rate of 12% compounded continuously. How much
money will you have at the end of 8 years?
Write in exponential form.
27.
1
𝑙𝑜𝑔4 2 = 2
28.
𝑙𝑜𝑔2 32 = 5
x
Write in logarithmic form.
29.
82 = 64
1 −4
3
30.
( )
= 81
32.
253𝑥 = 125𝑥−2
Solve each exponential equation.
31.
35𝑥 = 81
Solve each logarithmic equation. Round to the nearest ten-thousandth if necessary.
33.
log 4𝑥 = 3
34.
log 5𝑥 = 2
35.
Suppose that y varies directly with x and inversely with z, and y = 14 when x = 7 and z = 2. Write the equation
that models the relationship. Then find y when x = 18 and z = 9.
36.
Suppose that y varies directly with x and z, and y = 20 when x = 2 and z = 4. Write the equation that models the
relationship. Then find y when x = 10 and z = 3.
37.
Write an equation for the translation of y =
8
that has asymptotes x = 1 and y = 0.
x
38.
Write an equation for the translation of y =
6
that has asymptotes x = -3 and y = 2.
x
Describe the vertical asymptote(s) and hole(s) for the graph of each rational function.
39.
y
( x  7)( x  8)
( x  3)( x  7)
40.
y
x 2  9 x  18
( x  3)( x  3)
41.
Find the horizontal asymptote for the graph of each rational function.
y
a.
3x5  17 x
9 x5  2 x 4
b.
y
7 x  10
x3  8
Graph each rational function.
42.
2
𝑦 = (𝑥−4)
43.
(𝑥−1)
𝑦 = (𝑥+3)
Find the product. State any restrictions.
44.
3x3 x 2  6 x  5

x 2  25
x2
45.
y2  2 y
y 2  81

y 2  7 y  18 y 2  11y  18
Find each sum or difference.
46.
x
2

x  5x  6 x  2
47.
4x 1
3

2
x 4 x2
48.
y
2

y 1 2 y  2
49.
3
2
 2
x3 x 9
2
Solve each equation.
50.
1
5
4
 2

x2 x 4 x2
51.
5
2

1
x 9 x3
2
Find the missing term of each geometric sequence. It could be its geometric mean or its opposite.
52.
5,
, 45
53.
2,
, 72
Determine whether each sequence is arithmetic or geometric. Then find the tenth term.
54.
56.
45, 90, 180, 360,…
55.
25, 50, 75, 100,…
2, 1, 0.5, 0.25,…
57.
1, 4, 7, 10,…
Find the sum of each finite arithmetic series.
58.
44 + 55 +…+ 99
59.
87 + 93 + … + 129
61.
6
Evaluate the following.
60.
7
62.
How many ways can the starting five players of a basketball game be announced?
63.
How many ways can 8 students stand in a single-file line?
C5
P3
Inside a bag of M&M’s there are 5 brown, 4 red, 3 blue, and 6 yellow. Inside a bag of Jelly Beans there are 4
strawberry, 5 cherry, and 6 pineapple. If you choose one candy from each bag, find the following:
64. P(brown M&M, cherry jelly bean)
65. P(blue M&M, strawberry jelly bean)
66.
The probability that an Algebra 2 student studies for a test is 75%. The probability that an Algebra 2 student
studies for a test and does well on the test is 45%. Find the probability a student does well on a test, given he
studied for the test.
67.
The probability that it will snow tomorrow is 60%. The probability that it will snow tomorrow and school will be
cancelled is 18%. Find the probability school will be cancelled tomorrow, given that it snows.
The results of a race of athletes are normally distributed with a mean finishing time of 72.2 minutes and a standard
deviation of 6.8 minutes.
68.
Find the percent of athletes with finishing times between 58.6 and 72.2 minutes.
69.
Find the percent of athletes finishing with a time less than 58.6 minutes.
70.
Find the percent of athletes finishing with a time greater than 79 minutes.