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

modicalm@pwcs.edu

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.