Math 120 B

Midterm 2

Thursday, May 10, 2018

Name:

UW email address:

Problem 1 8Problem 2 6Problem 3 8Problem 4 10Problem 5 8Problem 6 10

Total 50

• There are 6 problems spanning 5 pages (your last nonempty page should be numbered as 5).

Please make sure your exam contains all these questions.

• You are allowed to use a TI-30x IIS Calculator and one double sided hand-written 8.5 by 11

inch page of notes.

• You must show your work on all problems (unless explicitly instructed otherwise). The cor-

rect answer with no supporting work may result in no credit. Put a box around your FINALANSWER for each problem and cross out any work that you don’t want to be graded. Give

exact answers wherever possible.

• Any student found engaging in academic misconduct will receive a score of 0 on this exam.

• Scratch paper is available. Please do not use your own.

• You have 80 minutes to complete the exam. Budget your time wisely. Do not spend too muchtime on an individual problem, unless you are done with all the rest.

GOOD LUCK!

1. (8 pts.) For each of the following questions, solve for x. If there are multiple solutions, find all

of them. Leave your answers in exact form.

(a) log4(2x+ 4) = 3

(b) e5|x+2|+1 = 12

1

logo 2 4 3 469462 47 432 4 64

2 GO

30

e51 21 1

12 luce 51 21 tl lnl2

51 21 1 lick

1 21 41215xyz ln

S

2 bs

2. (6 pts.) Let f(x) = x4 + 5x�1. Suppose we take the graph of y = f(x) and do three things:

• First, shift it 3 units down.

• Then, stretch it horizontally by a factor of 2

• Then, reflect it with respect to the x�axis

Write a function g(x) for the new transformed graph.

3. (8 pts) Write a multipart rule for the function f(g(x)), where f(x) = |4x� 3| and g(x) = 2x+ 1

2

ye x4 5 19 9 3 y x4 513

ye It 5 3 EY

ye E 5 3

fade4 3 4 3 o

4 3 4 320

fegan4 2 4 3 412 1 3 0

4 2 1 3 4 2 1 3 0

8 11 8 41704gGD8 1 8 1 08 41 xx f8 1 x c t

4. (10 pts.) You are given the function f(x) =p4� x2, �2 x 0.

(a) Draw the graph of f(x) on Grid 1.

(b) Find a formula for y = f�1(x).

(c) Find the domain of the function y = f�1(x)

(d) Find the range of the function f�1(x)

(e) Draw the graph of the function y = f�1(x) on Grid 2.

Grid 1 Grid 2

3

y

ye fix y2txE 4

ye 45 2 5 4 x2 I 4 y2x I 4 2

so y 5472 iffy beeXE ORange of 4 1 so 0 EXE 2

Domain of 46 so ZE X E O

rI

5. (8 pts.) Lucky’s owner (from quiz 4) decided to use a linear-to-linear rational function to model

Lucky’s weight. She notices that he weighed 1 kg when he was born, 9 kg when he was 18

months old and 11 kg when he was 2 years old.

(a) Find a linear-to-linear rational function f(t) giving Lucky’s weight when he is t years old.

Lucky

(b) What is Lucky’s weight going to be when he is 10 years old according to her model?

(c) What weight is Lucky approaching as he gets older (assuming that he lives for a very long

time)?

4

NAH DANAH

fcts.AEEtcfco L Bz I Btc

gel57 9 A l.sc 9 sA.l 5tB1 stc B Stg421 11 AIB 11 2AtB 22411CEtcA Ai1.5 8 13,5 3A 16C 27

130 A 2 loc 22 3A 15C 33e 6 c G so 13 6 A 33 15

644741 tt 6 3Ae 41

tlo 41 10 626lb

Find her asymptote41

Ye T so approaches 41 lbs

6. (10 pts.) (Ostroff Aut. 16) The rent for a one-bedroom apartment in Beattle is growing expo-

nentially (Even though the city is filled with bees).

(a) In the year 2000, the rent in Beattle was $1020, and it increases by 2.3% per year. Write a

function f(t) for the rent in Beattle t years after 2000.

(b) The average monthly rent in Tickoma is also growing exponentially.

In the year 2007, the rent in Tickoma was $500 less than the rent in Beattle.

In the year 2016, the rent in Tickoma is $1000.

Write a function g(t) for the rent in Tickoma t years after 2000.

(c) When will the rents in Beattle and Tickoma be equal? (Round your answer to the nearest

year.)

5

tfCt 1020 1.023

f 7 1020 1.02377 1,196g 7 l 196 500 696

g 16 1000

get Aobtg 71 696 to 67 696

91161 1000 A b61000

A b9 1.436be1.436be 1.041so to 696 b

7Ao 696 6549 525

gct fat as gas525020 1.023 t 525C1.041 t µtbn 1020 t flu 1.0237 lu 525 t thr 1.041t la 1.023 lull 041 luc 525 luc 1020t luff 1 4 2201 tho 9831 410.514

C 66 t 38yearsso in 2038