Class Ib:
Name:
MATH 1090-001
S.,’--s
Ii
Midterm 2.V2
Spring 2013
Instructor: Katriria Johnson
o SHOW ALL. WORK. No points will be given for answers without justification.
o Scratch paper will be provided by the instructor, just ask. Scratch work will not be
graded, record all work that is part of your solution on this exam.
o Make sure your work is organized and legible.
o Use a PENCIL, erase errors.
o NO CALCULATORS, NOTES, PHONES, NEIGHBORS, ETC.
o Answers should be simplified (reduced.)
o Box or Circle your final answers.
Prob.
1
2
3
4
5
6
7
Total
Score
/20
/10
/10
/16
/10
/14
/10
/90
1. Find the inverse of f(x) =
x+3
x—2
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-
2. If the demand function for a commodity is given by p =99— 2q q
2 and the supply
function is given by p =q
2 +lOq+95, find the equilibrium quantity.
Leave your answer in exact form; don’t worry about rounding to the nearest integer.
—
0
lk\2-O
(%to%r)
()2
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—
2
22
2.
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c -3±
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3. Given the function, g(x) =
x—2
2—5x
a) What is the domain of g? Write your answer in interval notation.
b) Identify the vertical asymptote(s).
c) Identify the horizontal asymptote.
d) Find the x-intercept(s) of g’
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e) Find the y-intercept of g’
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f) Sketch the graph of g. Be sure to label all asymptotes and intercepts.
2.
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2
2 + 320x + 200 and the price per unit is
4. The cost of producing x units is given by C(x) 4x
=
(720—6x).
a) Find the revenue function, R(x). Write your answer in standard form.
z
12O,i
-
-120% - to%
2
b) How many units must be sold to get the maximum revenue?
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c) Find the profit function, P(x). Write your answer in standard form.
—
p():
*120y. —
2
-L,,c.
(
242O
.i2oo)
—2oo
’+LO
2
-O’
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d) What is the maximum profit?
/
-O(
20
2
-4D’t4oo)-2oo
— (- 400o)
* 3Soo
2
?(‘c) -o(’-2o’)
\O0
c,oo
—
200
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5. Identify the base function and describe the transformations.
a) f(x)=,J—(x—1)+2
Base function is y
Transformation(s):
O4
U?
2
12x÷16
b)g(x)=3x
—
2
—
Base function is yt
Transformation(s):
( -2)
-c,c*or
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*‘\
c
2
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b
—
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c
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7. Give the function h(x) =
x —1
2
—x
x>5<x
—2
1
x—2
a) What is the domain of h? Write your answer in interval notation.
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-g
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b) Evaluate:
i) h(-2)
ii)h(O)
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o—
iii) h(3)
Is
iv)h(6)
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OmC(
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