ALGEBRA 2 – SPRING 2016 FINAL EXAM REVIEW
Name: _______________________________
Period: _________
Read the instructions carefully. The letters represent individual questions, not answer choices.
Show your work on separate sheet of papers.
Go over your notes;
Use your exponent chart
Quizzes will be given based on the review:
May 19 –
May 24 1. Write the equation in exponential form.
A. log 8 64 = 2
1
B. log 3 = −2
9
A.
B.
1
C. log 5 125 = −3
3.
Determine the horizontal asymptote(s) and the
vertical asymptote(s) for each function. State the
restrictions.
A. 𝑦 = −
C.
y=
4.5
𝑥+2
J.
K.
B.
4
𝑥(𝑥−2)
𝑦=
D.
𝑝−5
𝐺. 𝑓 (𝑥 ) =
I.
+3
𝑝2 −13𝑝+40
E. 𝑦 = 2 +
2. Give an example of an equation that will show
translation of left 2 units and down 3 units using the
following functions:
𝑥
𝑓(𝑥) = log 2 𝑥 + 4
H.
y=
A.
B.
𝑥−7
𝑦=
3𝑥 2 +4𝑥+2
𝑦=
C.
5𝑥 2 −𝑥+3
𝑥+1
D.
2𝑥−3
x +6
x + 3x -10
2
5
𝑥
𝑦 = −3 +
𝑦=
E. 𝑓(𝑥) =
4
𝑥+5
4𝑥
2𝑥+3
2𝑥+2
3𝑥−4
F.
(𝑥+6)(𝑥+2)
𝑦 = (𝑥+9)(𝑥+7)
G. 𝑓(𝑥) = log 2 𝑥 + 4
f(x) = 5(x+2)-3 is
y=
H.
Page | 1 Alg2
D.
4. Find the x-intercept and y-intercept of each
function.
3
F. 𝑓 (𝑥) =
3
𝑓(𝑥) = √𝑥 − 3 + 1
𝑓(𝑥) = 𝑒 𝑥
C.
𝑓(𝑥) = 𝑥 2 − 1
3
D. 𝑓(𝑥) = √𝑥
E.
𝑓(𝑥) = log 5 𝑥
x +2
x 2 + 7x
5.
Find the solution for each.
𝑥
B.
A.
C. 2 =
𝑥+2
𝑥−3
6.
A. With your new lawn mower, you can mow a lawn
in 5 hours. With an older mower, your friend can
mow the same lawn in 2 hours. How long will it
take you to mow the lawn, working together?
B. Cindy can finish her 20 problem homework in 2
hours. Mark can finish the same number of
problems in 2.5 hours. Working together, how long
will it take them to complete a 20-question math
homework?
3
D.
−2
= 𝑥+7
3
9
=
x +1 4x + 5
7. A. An initial population of a bird species increases at
an annual rate of 22%. Write an exponential function to
model the bird population. What will the approximate
population be after 5 years?
B) Roland earned $1500 last summer. If he deposited
the money in a certificate of deposit that earns 4%
interest compounded monthly, how much money will he
have after 2 years?
For (C and D) :
1
Use the formula: 𝑦 = 𝑎( )𝑥 , 𝑎 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡,
2
𝑥 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 ℎ𝑎𝑙𝑓 − 𝑙𝑖𝑣𝑒𝑠 =
𝑡𝑖𝑚𝑒
ℎ𝑎𝑙𝑓−𝑙𝑖𝑓𝑒
𝑦 = 𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑎𝑚𝑜𝑢𝑛𝑡
C) There are 80 grams of Cobalt-58 which have a halflife of 71 days. How many grams will remain after 213
days?
D) Two hundred ten years ago there were 132,000
grams of Cesium-137. How much is there today? The
half-life of Cesium is 30 years.
8. Use synthetic division to find P(–2) for
A. 𝑃(𝑥) = 𝑥 4 − 6𝑥 3 − 2𝑥 2 + 7𝑥 + 10
B. 𝑃(𝑥) = −𝑥 2 + 5𝑥 − 3
C. 𝑃(𝑥) = 2𝑥 3 − 5𝑥 2 + 𝑥 + 8
10. For each option, what total will you pay back
if You borrowed $40,000 for 3 years at 8%
A.
B.
C.
D.
compounded annually.
compounded semi-annually.
Compounded quarterly.
Compounded monthly.
Then decide, which option gives you the least
interest paid.
Page | 2 Alg2
9. What is the simplified form of :
A.
B.
C.
𝑥 2 +4𝑥−5
𝑥 2 −25
3𝑥
2
− 𝑥 2 −25
𝑥−5
11. Sketch the Graph each of the following
12. Identify the range of the function,
functions.
below.
A) y =
B) y =
f ( x) , graphed
(x + 3)(x - 4)
x +2
(x + 3)(x + 4)
x-2
C) y =
13.
x +2
(x + 3)(x - 4)
Suppose a transformation of the parent
function
is given as
where
. Determine the effect the
transformation has on the range of the
function.
A. The range remains the
same.
B. The range becomes
instead of
14.
The area of a rectangle can be represented by
x – x – 6 and the height of the prism is x + 2. What
would represent the length?
2
,
C. The range becomes
instead of
.
D. The range becomes
.
instead of
.
16. What are the minimum and maximum values of each
15.
Determine which binomial is not a factor of
.
function with the given intervals:
A.
A. x + 4
C. x – 5
B. x + 3
D. 4x + 3
Page | 3 Alg2
B.
on the interval
, on the interval
17. Solve:
A) 5(2x-9)= 125
18. Classify each function as exponential growth or
decay:
B)
C)
2
(2𝑥 − 1)3 + 1 = −3
. Note:
exponent
2
3
A)
r(x)=
is an
3 -3x
e
4
B)
r(x)=
4 -3x
e
3
3 3x
e
4
C)
r(x)= 4e-3x
E)
2
u(t)= -7.0( )t
3
F)
3
u(t)= -7.0( )t
2
G)
u(t)= 7.0(.8)t
H)
10
u(t)= 7.0( )t
9
D)
D) 5𝑥 = 53𝑥−20
E) 3𝑥 ∗ 93𝑥 = 35𝑥−1
r(x)=
F) 25𝑥+2 = 3125𝑥
𝐺) 5(3𝑥−5) = 625
H) 16𝑥+8 = 64𝑥−2
I)
2 = log 3 (𝑥4)
J)
log 5 (𝑥 − 2) − 4 = −3
K)
log 4 𝑥 = 2
19. The function
models the daily profit y, in
thousands of dollars, x months after a small business begins
to operate. Graph the function and interpret the domain and
intercepts.
20. If the function f(x) = 3x is transformed to
f(x) = 3x-2+5, which of the following changes?
A)
B)
C)
D)
21. Find the inverse function of each of the
following:
A. 𝑓(𝑥) = √𝑥 + 2 – 5
3
B. 𝑓(𝑥) =
C. 𝑓(𝑥) =
1
4
√𝑥 + 3
4
√𝑥−6
3
− 2
Parent’s signature: __________________________________
Page | 4 Alg2
the domain and range
the horizontal asymptote and domain
the vertical asymptote and range
the horizontal asymptote and range