Math 110: Final Exam Version AFall 2018

• Calculators are NOT allowed.

• Please code true/false and multiple choice answers on a scantron. These are questions 1 - 10.

• Since you have test version A, please code the ”Page Number” on the scantron as 1.

• No partial credit for multiple choice / no work needs to be shown.

• For short answer questions, you must show work for full and partial credit.

• Multiple choice and true / false problems are worth 4 points each. Free response questions are worth6 points each.

• Sign the honor pledge below after completing the exam.

• Please put all work to be graded on the test itself.

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1

key

1. The graph of the function y = f (x) is shown below.

Use transformations to draw the graph of y = � f (2x) � 1.

A B

C D

2. Simplify and write the answer without negative exponents.

32x�7y�8

x�2y2

!2/5

A.4

x2y4

B.1

4x2y4

C.32x14

y16

D.64

5x7y4

E.64y12/5

5x18/5

2

reflect across x axis

shrink horiz by 12do n by L

T v

ati s II

3. Find the equation of the graph.

A. y = (x�4)(x+3)(x�6)

B. y = (x�4)(x�1)(x�2)

C. y = (x�4)(x+5)(x�1)(x�2)

D. y = (x+3)(x�6)(x+5)(x�4)

E. y = (x+5)(x�4)(x+3)(x�6)

4. Find the equation of the graph:

A. y = � 110

(x + 2)(x � 3)

B. y =1

10(x + 2)(x � 3)

C. y = � 110

(x + 2)2(x � 3)

D. y =1

10(x + 2)(x � 3)2

E. y = � 110

(x + 2)2(x � 3)2

5. Find the equation of a line that is perpendicular to the line 3x+ 4y = 7 and goes through the point (6, 5).A. 3x � 4y = �2B. 4x � 3y = 7C. 4x � 3y = 9D. 4x + 3y = 7E. 4x + 3y = 39

3

v A at 3 x 6

X intercept at x 5 2 4

Zero of degree2 at x 2Zero ofdegree I at x 3negative lead coeff

9 40 x 1 2 21 3

O

O 4y 3 1 7

y Z xt LyMz Ygy Yg x t b

5 45.6 5 5 8 6 b 3

y Iz X 3

3g 4 9 4 3y g

6. For the functions f (x) = x2 + x and g(x) =1

x + 4, find an expression for f � g(x).

A.1

x2 + x + 4

B.1

(x + 4)2 + x

C.x + 5

(x + 4)2

D.x2 + xx + 4

E.x3 + 4x2 + 1

x + 4

7. Solve the inequality. Write your answer in interval notation.2|3 � 2x| + 1 > 5

A. (0,1)

B. (�12,

12

)

C. (12,

52

)

D. (�1, 12

) [ (3,1)

E. (�1, 12

) [ (52,1)

8. The two points (3, 4) and (�1, 2) lie on a circle, on opposite sides of a diameter. Find the equation of thecircle.

A. (x � 1)2 + (y � 3)2 = 5B. (x + 1)2 + (y + 3)2 = 20C. (x � 1)2 � (y � 3)2 = 25

D. (x � 1)2 + (y � 3)2 =p

5

E. (x + 2)2 + (y + 1)2 =p

20

9. A model rocket is launched and its height in meters at time t seconds is given by the equationh(t) = 6t � 3t2. Find the time(s) at which the height of the rocket is 2 meters.

A. t = �2B. t = 1C. t = 2D. t = 1, 2

E. t = �1 +p

33, 1 �

p3

3

4

f glx f IIa

0 t y

I4,2

t II 14

I t xt4 Xt y 2

2 3 2 1 4 3 2x 3 2xt

13 2 172 z

3 2x L 2 or 3 2x 72

2x L 5 or 2 7 I

X Iz or X I

fcenter at midpoint

3 4 1,3

radio 1 2 1 1 3 Z

O II if

1 t y 32 5

2 6 t 3 EZ

31 2 6 Et 2 0medor O m f 6 I 367413312gue e 213HMP

c gl 2

It

10. Use log properties to write the following expression as a single log. You may assume that all variablesare positive.

12

log(x + 5) � 8 log(x) + 2 log(y)

A. log

(x + 5)1/2

x8y2

!

B. log

(x + 5)1/2y2

x8

!

C. log

(x + 5)y8x

!

D. . log⇣

12 (x + 5) � 8x + 2y

⌘

E. log⇣(x + 5)1/2 � x8 + y2

⌘

5

log Xt logx8 logy12O

log t logy

log2

ya

lugft 5

2 y28

11. TRUE or FALSE and justify your answer.

(a) log(x � y) =log(x)log(y)

. (circle one) TRUE or FALSE

Explanation / Counterexample

(b) The equation 4|x + 5| < �2 has no solutions. (circle one) TRUE or FALSEExplanation / Counterexample

(c)p

a2 + 25 = a + 5. (circle one) TRUE or FALSEExplanation / Counterexample

6

Each part4 pts per

part12 pts total 2 pts answer

2 pts explanation

for exark if 10 y 10

left side is lusco DNE

right side is 4

O

1 151 c Ican't Love negative cbs value

So no solutions

0a I

oft 526 It 5 6

Since 26 1 62 36

12. Find the domain of the function f (x) = 2p

x2 � 3x � 10. Write your answer in interval notation.

Answer:

13. The population of spiders on an island (in millions) is growing according to the equation y = 30e0.05t.If this growth rate continues, find the amount of time it will take the population to double. Write youranswer in a form that you could type into your calculator.

Answer:

7

x 2 3 10 O 2 pts inequalityEan get fullcredit2ps x 5

X 5 Xt 2 70 without writingthis2 down ifotherwork is

1pteach correctO O

torn2 5

3 to ye 6

C P 2 u DD 2pm anne l for edpt errors

9 30 eOos t

G 0 30 eOtt

2 pts plug in 60 fer y

o 05 t I pt2 eo os t pt Ln of eachsideIn 2 In e

In 2 0.05 t I p t

C In 2I pt answer0.05

In 2

14. Simpify:

16 + x

� 16

x3

Answer:

15. Solve for y: y � 4 =p

31 � 6y

Answer:

8

due to notdistributing

nesohesush but1 if get an else correct

2 Gtx2 pts for multiplying by

reciprocal2ptg for adding factions

6to 4 Eto E

E

Eg 3

X6 Gts x6a fans

3 1216 8

t216A 2 pts correct find answer

y 417 yt or

y 8ytl6 31 69 check y J

y 2g15 0 s 4 E TE

y 3

yes gt3O

zc I 5

wy I y 3 y 549 X

extraneous

9 5u if did not exclude

extraneous solution

16. Solve for y. Your answer should be in terms of x.

x =2 � y

3y + 1

Answer:

17. Find the values of the expressions. Write DNE if the value is undefined.

(a) log218=

(b) log9 3 =

(c) log4 0 =

(d) ln e2 =

(e) 5log5 10 =

9

3yH x 23 4 3ytiy

2 X

3g 1 X Z Y W Y 3 1

3 Xt X 2 y

inIy

3g x y Z X

x uy 38

z Xr

3 1

I pt eachno partial credit3 z

3Ig pt for free

Iz g 2 3 since only 5 parts

DN E 40 0 has no solution

2 Iogee22

10

18. Choose ONE of the problems below and SET UP a system of two equations in two unknowns that youcould use to solve it. You DO NOT need to finish solving the problem. Please circle the problem youchoose.(a) Xavier and Yolanda leave at the same time and bicycle towards each other from towns 40 miles

apart. Yolanda bikes 2 miles per hour faster than Xavier. They meet somewhere in between after 2hours of biking. How fast do they each bike?

(b) A chemical company makes two brands of antifreeze. The first brand is 35% pure antifreeze, andthe second brand is 60% pure antifreeze. In order to obtain 70 gallons of a mixture that contains40% pure antifreeze, how many gallons of each brand of antifreeze must be used?

10

3 ptsdistance rate the each ear

tF

gallonsliquid

y 0.60960

lporet.TOTO

19. The amount of co↵ee beans in a co↵ee shop decreases at a constant rate. On November 4 there were 105pounds of co↵ee beans in the shop. On November 11 there were 70 pounds of co↵ee beans.(a) Write an equation to express the pounds of co↵ee beans C in terms of time t since the end of October.

Answer:(b) If this rate continues, and no more co↵ee beans are brought in, when will the shop run out of co↵ee

beans?

Answer:

20. A wedding dress was purchased for $1200. Suppose that its value decreases by a fixed percent eachyear, and two years after purchase, the value is $900. Write an equation to express the value V in termsof the time in years t since purchase. Your equation should only have two variables: V and t.

Answer:

11

Ito m YET 78 5

5 ttb105 5 4th

b I 051 20 125

1 if write2 pts slope E in terms

5 t t 125 1 if wrong s5h of c

2 pts intercept

0 5 Et 125 125 5 t C 25

I pt set c O

pt answer

25 days Nov 25

i ig

D 1200C It Gz 1t

y L zoo TE t

iZ e Z hear zr LE FEI

2pts r

y 1200t I pt final ante

21. Find the x and y intercepts of the graph of y = log3(x2 + 1) � 2

x-intercept(s): y-intercept(s):

22. Solve the system of equations:

x2 + 3y = 4

2x � y = 4

Answer:

12

X intercept 0 1 1 2 1 z 2 1053 721

pt s

Py f 52 1 8

2 3 x tr Izak

2 ptssolve

9 1053 Ott Z 0 2 2

for X1 for y intercept

i o

gon'T 1 pt pl 5 n

if leau a s as

2 pH sole for Y 109311 if switchx ay

intercepts

58,01f 8,0 10 2

2 pts gettingg 2 4 x 1 3 2 4 4 to fn of

one variable

2 6 12 4

t GX 16 0

1 811 23 0x 8 x 2

8 y zC 8Y y

20

7 2 y zczj y y 0

C 8 20 and 4 pts answer 1 pt each2,07 1 if pairs mismatched