Math 1090.003 Midterm 03
Spring 2016
• Remove headphones and hats during the exam.
• Show all work, as partial credit will be given where appropriate. If no work is shown, no credit will be given.
• All final answers should be written in the space provided on the exam and in simplified form.
When needed, give your answer as an exact amount, i.e. a fraction or symbolic expression, except for dollar amounts which should be rounded to the nearest cent.
• You may ask for scratch paper. You may use only the scratch paper provided.
Please transfer all finished work onto the proper page in the test. We will not grade the work on the scratch paper. Box your final answer to each problem and write it on the lines in the right-hand corner, if provided!
• Scientific calculators are allowed on this exam. Absolutely no graphing calculators.
No other electronics are allowed.
• Formula sheet: The use of the back and front of one piece of 8 x 11 paper is allowed on the exam.
• If your phone is out during the exam it will be considered a cheating offense your phone away!
put
PLEASE DO NOT WRITE BELOW. THE TABLE IS TO BE USED FOR GRADING.
Problem Score
1
2
3
4
5 ‘iD
6
7 2-0
Bonus 5
Total 105
1

05 April 2016
Math 1090.003
1. [20 points] Label your axes and curves!
(a) Graph the function f(x)
3X
(-I ‘-)
C
(i)
-ccs
4-
5
I
-.
10
>c
I rt
O frYi2.
—5 a
-10’
The domain of the function is:
2
(rS.
—
< f(x)
(b) Graph the function g(x)
=
2(3_x) + 1.
(If you choose to graph intermediate functions, label your solution clearly.)
I p+ jkf
_,( x)Lj tu” l,-Lvr wtk fly f(-’) rt..
c,-i-ceKh
Lt4
J2
2fC—Y)
2(3
X)
—4-—
-
—10
.L_-
-
—5
-.________________
a
5 10 x
=.
• ctii’—f
I i tv’sfo
—10
2 (-x)I
(o, 0
(jif) f(.
K) t •2.
c
The domain of the function is: vcraL1
c_I
) z)
6)
2
(0
C
Cl
72
(L

( t)O
:
C4 2-)
Math 1090.003
(c) Graph the function h(x)
= log
-10 -5
5
I cl e-
05 April 2016
—
5
—.
10
I.
P+
—10
The domain of the function is:
cr2,
(d) Graph the function k(x) (x + tions, label your solution clearly.)
1)
—
2. (If you choose to graph intermediate func
h(X) io1i()
-
(ovt
1
yv-fcI I% dowr
1
L.
k(x I)
-
-
Sktf(
(QO)
L)
L2)1)
(4)2) (7)) domain of the function is:
ALl
3
2 ( O)-a)
—1
(o
(
1
5 10
) p-
WJV
2
(-AA aiv ta-i o rLtS

05 April 2016 Math 1090.003
cLU
2. Use properties of logarithms to expand the following expression into simplest terms.
(/x
—
4
5 pt.
([z)
f (x [10 points]
(o(
()(-4) pt
3. Use properties of logarithms to condense the following expression into simplest terms.
I(cz( tx3+)+
Iog(x
—
3) + Iog(x) lOg4().
\
[10 points]
)ocj c
[‘‘ pt

____
Math 1090.003
05 April 2016
CO(AAd
4. Given
1(x) = x + 1 + 2, compute f’(x).
f)-
@—)
Y
---
+ 2
(x-Z
(
-
[15 points]
)r)_ j
3
=
+ j
5. If 1(x) 3
—
2x and g(x) = —(x
—
3), compute (go f)(x) and (To g)(x).
Question: Is (g o 1)(x)
=
(1 o g)(x)? If yes, what does this mean?
[10 points]
—
I
cx
(-2k)
C
2
-
I
5 cQ ±S fA

05 April 2016
Math 1090.003
Iabe1
6. For the piecewise function, fill in the table of points and then sketch the graph.
axes and curves!
Label your
[15 points] x2,
—1<x<2,
—2x
—
2, x < —1
-c.
X)J fr € A
—6
4
—4 —2
5
I
I
3pL
—Ia--
6
—5
-
I
--I

Math 1090.003
05 April 2016
7. Word Problems
(a) The population of Smalltown has an initial population of 14,000 in the year 2000. The population grows at a rate of 3% per year. Assuniing exponential growth, the population equation is
(+)z VT)
[10 points]
What is the population in 2002? Round to the nearest person.
pCz toz— 2000 e o,0•,
2Y1
J4G00 fZ_E
-
(b) Sound intensity is given by the formula
/3
=
10 log
(h), where I is the reference intensity, just below the threshold of hearing, /o
=
10_16 watts per square centimeter.
[10 points]
What decibel rating is a sound of intensity I
=
10’s W/cm
3( tD)
7

Math 1090.003
05 April 2016
(1)
Bonus: What are the three types of transformations? Use mathematical eqUations to describe each transformation.
[5 points] sUi.df
2) sfc €
3) p-Ls for
8