FA 16-17
Attn: Upcoming Functions Analytic Geometry students,
All Functions Analytic Geometry students should complete this assignment prior to the
first day of class. During the first week of school, time will be spent answering questions
students may have on the material covered in this packet with the understanding that
they will be assessed on these topics starting the second week of school and
throughout the year. This review will be in addition to covering new material from the
first chapter, Functions and Their Graphs.
Functions Analytic Geometry is a one-year preparatory course for AP Calculus BC. This
course is designed for students who have successfully completed the standards for Pre
AP Algebra II /Trigonometry. Throughout the year students will learn various objectives
which will challenge them and will help to enhance their problem solving skills.
This packet was devised to help students be successful not only in Functions Analytic
Geometry but in all subsequent math courses as one of the goals of this class is to
prepare students for the challenge of AP studies in mathematics. It is essential for
students to master the skills covered in this packet. You must be able to understand and
apply this information throughout the school year.
To best prepare for this class, it is recommended that students complete this packet
within two to three weeks directly before school starts. Calculators should not be used
to complete this packet. If some concepts are challenging and require a refresher of the
material, two good sites for information are www.khanacademy.org and
www.purplemath.com.
If you have questions regarding the nature of this course, the summer assignment or
anything else, please feel free to email me. In the summer I usually check my email
once a week. I will respond as soon as possible.
Good luck! Enjoy your summer vacation!
I look forward to meeting you in the fall!
Ms. Modica
FA 16-17
Section 1 - FACTORING
Factor the following problems.
a. x4 – 7x2 – 8 b. x2n – 2xn + 1 c. x4n – 6x2n + 9
d. 3 2( ) 2 f x x x x e.
3 2
( ) 4 14 20 f x x x x
f. x 3 + 8 h. 27x³ + 8
i. a3 – 27 j. 8x3 - 125
FA 16-17
Solve each quadratic equation by completing the square.
a. 0262 xx b. 027244 2 xx
c. 0423 2 xx d. 24 16 7 0x x
FA 16-17
Section 2 - FUCNTIONS
Use the information in the box below to answer questions parts a – h below.
Given the following functions:
( ) 3 2f x x ( ) 2 5g x x 2( ) 3 5 4h x x x 3
( )2
j xx
2
1( )
1k x
x
3( )m x
x
5 1( )
1
xn x
x
Find each of the following composed functions and state the domain:
a. ( )h f x
d. ( )f g x
b. ( )j n x
c. ( )n f x
e. ( 3)f m x
Find the inverse of:
f. f(x) g. g(x) h. n(x)
For the following pairs of functions show that ( )( ) ( )( )f g x g f x x
i. ( ) 2f x x ; 1
( )2
g x x
k. ( )f x ax b ; 1
( ) ( )g x x ba
j. 3( )f x x ; 3( )g x x
l. ( ) 3 7f x x ; 7
( )3
xg x
FA 16-17
Section 3 – POLYNOMIALS, RATIONALS, EXPONENTIALS and LOGARITHIMS
Simplify.
a.x x
x x
x x
x x
2
2
3
2
7 10
6
4
8 12
b.
3 2
2 2
64
4 16 16
x x
x x x
c. x
x
x
x x
2
8
2
6 162 d.
3 5
2 6
4 2
5 15
y
y
y
y
g. 3 7 4( 2 )x x h. 4 2 2 3 5( )( )r s r s i. 6 2
3
x y
y
j. 10
52
x
x
k.
3 24 3 3
5 3
2a b ab
b a
l. 4 3 2 3 3( 5 )( 2 )x y a b
m. 481x n. 5 4 93 32x y z o. 4 4 33 56x y z
p. 9 2 124 625x y z q. 1
9 6 3( 64 )x y r. 1
6 10 5(64 )x y
Evaluate each expression.
a.
24
5
b. 3
481 c. 2 3
3 4(100 ) d. 2
1 23 3
FA 16-17
Indicate your answer below by circling the best response.
a. What is axlog3 written in exponential
form?
(a) 3x = a
(b) a3 = x
(c) ax = 3
(d) 3a = x
b. The equation y = ax expressed in
logarithmic form is:
(a) ylogx a
(b) yloga x
(c) alogx y
(d) xlogy a
c. The expression log 12 is equivalent to:
(a) log 3 + 2 log 2 (b) log 6 + log 6
(c) log 3 log 4 (d) log 3 – 2 log 2
d. The expression log 4x is equivalent to:
(a) 4 log x
(b) log 4 + log x
(c) (log 4)(log x)
(d) log x4
e. The expression b
alog
3
is equivalent
to:
(a)
blog
alog3
(b) )bloga(log3
1
(c) )bloga(log3
(d) blogalog3
f. The expression blog2
1alog is
equivalent to:
(a) )balog(
(b) balog
(c)
blog
2
1alog
(d) ablog
g. Which of the following equations is equivalent to 5log33log73logx ?
(a) 3x7 53
(b) 125)7x( 3
(c) 37x 53
(d) 1521x3
FA 16-17
Solve each equation.
a. 2214 44 xx
b. 493
2 xx
c. 3log 4 2x
d. 4log 8 x
e. 8
2log 5
3x
f. 5
2
4log
25x
g. 6 6 6log 2 3 log 12 log 3x
h. 2log31log3log2 333 xx
i . 2ln11ln53ln x
j. 4ln3ln1lnln xx
k. 1log216log xx
l. 21log2log xx
FA 16-17
Section 4 – EXPONENTIAL, LOGARITHMIC, NATURAL LOG and e GRAPHS
Create a table of values for the parent graph, graph (remembering transformations), and
state the domain, range and asymptote for each of the following:
a. 2xy b. 22 xy c. 2 xy d. 2 4 xy
D: D: D: D:
R: R: R: R:
Asymptote(s): Asymptote(s): Asymptote(s): Asymptote(s):
Hint (logarithm function is the inverse of an exponential function)
e. 2logy x f.
2log 2 y x g. 2log ( 2) y x h.
2logy x
D: D: D: D:
R: R: R: R:
Asymptote(s): Asymptote(s): Asymptote(s): Asymptote(s):
x -3 -2 -1 0 1 2 3
y
x
y -3 -2 -1 0 1 2 3
FA 16-17
i. xy e j. 2 xy e k.
1 xy e l. 1 xy e
D: D: D: D:
R: R: R: R:
Asymptote(s): Asymptote(s): Asymptote(s): Asymptote(s):
Hint (logarithm function is the inverse of an exponential function
m. lny x n. ln( 3) y x o. ln 2 y x p. ln( )y x
D: D: D: D:
R: R: R: R:
Asymptote(s): Asymptote(s): Asymptote(s): Asymptote(s):
x
y -3 -2 -1 0 1 2 3
x
y -2 -1 0 1 2
FA 16-17
Section 5 – TRIGONOMETRY
Fill in the values of the unit circle below:
In the ovals – write the degree value
In the rectangles – write the radian value
In the parentheses – write the coordinate value
FA 16-17
Using the unit circle, fill in the information below:
De
gre
es
Ra
dia
ns
sin
e
cosin
e
tan
ge
nt
co
se
ca
nt
se
ca
nt
cota
ng
en
t
0
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
FA 16-17
Graph the following trig functions.
a. siny x per: amp:
b. cosy x amp: per:
FA 16-17
38°
10
11
M P
Q
30°
16 10
G
H F
18
15
11
D B
C
c. tany x amp:______ per:_____
Solve each triangle by finding all of the missing side lengths and angle measures using the Law of Sines and/or the Law of Cosines. (A calculator may be used to answer these questions).
d. e.
f.