Class Ib:
Name:
MATH 1090-001
So\.Aicr
U_____________
Midterm 2.V1
Spring 2013
Instructor: Katrina Johnson
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SHOW ALL. WORK. No points will be given for answers without justification.
Scratch paper will be provided by the instructor, just ask. Scratch work will not be
graded, record all work that is port of your solution on this exam.
Make sure your work is organized and legible.
Use a PENCIL, erase errors.
NO CALCULATORS, NOTES, PHONES, NEIGHBORS, ETC.
Answers should be simplified (reduced.)
Box or Circle your final answers.
Prob.
1
2
3
4
5
6
7
Total
Score
/20
/10
/10
/16
/10
/14
/10
/90
2 + 80x + 250 and the price per unit is
1. The cost of producing x units is given by C(x) = 4x
(480
—
6x).
a) Find the revenue function, R(x). Write your answer in standard form.
gQ,c)
\z
)’
(so’
0
=
-
c’
() 4o’c
b) How marty units must be sold to get the maximum revenue
2
=
1
-(d
—
2o
440(
-_____
‘k 0
40
c) Find the profit function, P(x). Write your answer in standard form.
PCc)=
—
+4S0
—(2o..1o)
4 k’?tY’,( -
-
-
-
2oO
0’’# ‘-k00’. - 2O
d) What is the maximum profit?
P(.%):
-
-Q%l
—‘ci
—=
+40c’x
-4c’o
2c
-
—=
o
-o (.oo)
—
-LO
oo
%oo
-
.- Sooo —
-1400o -k-Sooo -S0
1ooo _2c,o
3-0
versioni
i
2. If the demand function for a commodity is given by p =100 4q q
2 and the supply
function is given by p =q
2 +8q+98, find the equilibrium quantity.
Leave your answer in exact form; don’t worry about roundirg to the nearest integer.
—
2
-
2
o
2
-
—
-
± -(iX-2)
2C2)
-
4.
-
-2-- -o
-
±
3. Find the inverse of f(x) =
4 iE
(-
x+1
x—5
J
versioni
2
4. Given the function, g(x)
X
=
—6
6-4x
a) What is the domain of g? Write your answer in interval notation.
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b) Identify the vertical asymptote(s).
2
c) Identify the horizontal asymptote.
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f
T
l
d) Find the x-iritercept(s) of g’
o
>
=b
0
•ç-
e) Find the y-intercept of g?
(= 0
-
I”,
f) Sketch the graph of g. Be sure to label all asymptotes and intercepts.
1’
version 1
3
5. Give the function h(x) =
—x
2
x —2
lxi
x>5
—2
<x
1
x—2
a) What is ‘the domain of h? Write your answer in interval notation.
b) Evaluate:
i)h(-2)
f—2
2
21
ii)h(O)
—2
iii) h(3)
1%-•.
4
‘,
flt
iv) h(6)
=
—
-
versioni
4
6. a) Given f(x)=x—3 and
g(x)=x2
—1.
I) Find (fg)(x). Write your answer in standard form.
.S(%)
=
=
2
2
-*
N
ii) bescribe the end-behavior of the function (fg)(x).
\
Is
oQ5
on
OY\
\Q
b)Given h(x)=g3x÷1,Qndk(x)=L Find (koh)(x).
2x
version 1
5
\
7. Identify the base function and describe the transformations.
a) f(x)=I—(x+2)I—1
Base function is y
Transformation(s):
‘
(4\€c\-ic,r
S\,:4
aOA
c-4
\e-%
\
2
2 —12x+15
b)g(x)=3x
Base function is y
Transformation(s):
--c\
((2
1
2 C’ 2’)
Sccir
o4
versioni
4
‘3
)
6