©Lynch, October 2015
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Math 150, Fall 2015
Exam 2 – Form A
Multiple Choice
Sections 3A-5A
First Name:
Last Name:
Student ID number:
Section Number:
Directions:
1. No calculators, cell phones, or other electronic devices may be used, and they must all be put away
out of sight.
2. There are 10 multiple choice problems on this exam, and each problem is worth 5 points. No partial
credit will be given.
3. There will be 5 bonus points awarded if you do all of the following (no partial credit):
ˆ bring the correct Scantron form,
ˆ correctly fill out your Scantron including your First and Last name on the TAMU class roster, the
Course #, Section #, student ID number, Signature, Date: Oct 2015, Exam 2, and your exam
version, Form A.
ˆ bring your student ID to the exam, and
ˆ turn in your exam and Scantron on time.
4. Together with the other part of the exam there will be a total of 110 points possible.
5. The Scantron will not be returned to you, so please mark your answers on this exam paper.
6. You may not discuss the contents of the exam with anyone until the exam is returned in class.
THE AGGIE CODE OF HONOR
“On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work.”
Signature:
Note: You are authorized to use a pencil, eraser, TAMU Scantron, and your own TAMU
student ID; use of anything else is a violation of the honor code. If you need any extra paper,
please ask your instructor or TA; do not use your own.
Scantron: Make sure the following is filled out correctly on your Scantron:
Last Name, First Name, Course #, Section #, UIN, Signature, Date: Oct 2015, Exam 2, Form A
©Lynch, October 2015
 √
 x−3
1. For f (x) =
5

2x2
(a)
Math 150 – Exam 2A
if x ≥ 4
if 3 ≤ x < 4 , calculate
if x < 3
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f (3)+f (7)
.
f (1)
7
2
(b) 10
(c) 1
(d)
11
2
(e) undefined
2. Describe the end behavior of the polynomial p(x) = (4x2 − 3x4 )(x3 + 8x).
(a) as x → ∞, p(x) → ∞, and as x → −∞, p(x) → −∞
(b) as x → ∞, p(x) → −∞, and as x → −∞, p(x) → ∞
(c) as x → ∞, p(x) → −∞, and as x → −∞, p(x) → −∞
(d) as x → ∞, p(x) → ∞, and as x → −∞, p(x) → ∞
(e) none of the above
3. Find the domain of the function f (x) =
√
x+1
x2 +3x−4 .
Give your answer in interval notation.
(a) [−1, 4) ∪ (4, ∞)
(b) (−∞, −4) ∪ (−4, 1) ∪ (1, ∞)
(c) [−1, ∞)
(d) [−1, 1) ∪ (1, ∞)
(e) (−∞, −4) ∪ [−1, ∞)
4. An open box is constructed from a 5 foot by 6 foot piece of cardboard by cutting squares of equal length
from each corner and turning up the sides. Write a function for the volume of the cardboard box in
terms of the length x of the cutout square. Restrict the domain appropriately.
(a) V (x) = (5 − x)(6 − x), Domain: (0, 5)
(b) V (x) = x(5 − x)(6 − x), Domain: (0, 5)
(c) V (x) = x(5 − 2x)(6 − 2x), Domain: 0, 52
(d) V (x) = x(5 − 2x)(6 − 2x), Domain: (0, 5)
(e) V (x) = (5 − 2x)(6 − 2x), Domain: 0, 52
©Lynch, October 2015
Math 150 – Exam 2A
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5. It takes the maroon pipe 6 days to fill a small stock pond. When the maroon pipe and the white pipe
are both used, it takes 30
11 days to fill the stock pond. How long would it take just the white pipe to fill
the stock pond?
(a)
(b)
36
11
15
11
days
days
(c) 3 days
(d) 5 days
(e) 6 days
6. Use the following graph of f (x) to find where the function is increasing. Also, determine if the function
is even, odd, or neither.
(a) [0, 5] ∪ [−5, 5], even
(b) [−8, −6] ∪ [2, 6], even
(c) [−6, −2] ∪ [6, 8], odd
(d) [0, 5] ∪ [−5, 5], neither
(e) [−8, −6] ∪ [2, 6], neither
7. Find the x-intercepts and y-intercepts of x3 y 3 − xy + |y − 5| + x2 = 9.
(a) x-int: -2,2
y-int: -4,14
(b) x-int: -3,3
y-int: -4,14
(c) x-int: -2,2
y-int: 14
(d) x-int: -3,3
y-int: 14
(e) x-int: -3,3
no y-int
©Lynch, October 2015
8. Let f (x) =
x−3
4x
Math 150 – Exam 2A
and g(x) =
x−3
x2 +x .
Calculate and fully simplify
(b)
2
x2 , D = (−∞, 0) ∪ (0, ∞)
2
x+1 , D = (−∞, −1) ∪ (−1, ∞)
(c)
(x−3)2
2x(x2 +x) ,
(a)
2
(d)
(x−3)
2x(x2 +x) ,
(e)
2
x+1 ,
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g(x)
2f (x) ,
and find the quotient’s domain D.
D = (−∞, −1) ∪ (−1, 0) ∪ (0, ∞)
D = (−∞, −1) ∪ (−1, 0) ∪ (0, 3) ∪ (3, ∞)
D = (−∞, −1) ∪ (−1, 0) ∪ (0, 3) ∪ (3, ∞)
9. Algebraically calculate and simplify the inverse function of the function f (x) = (3x − 6)2 + 5 , where
x ∈ [2, ∞]
(a) Since f is not one-to-one, it does not have an inverse function
(b) f −1 (x) =
1
(3x−2)2 +5
(c) f −1 (x) =
px
(d) f
−1
+6−5
√
(x) = 2 + x − 5
3
(e) f −1 (x) = 2 +
√
x−5
3
10. Test the equation xy 3 = 3|y| − x2 for symmetry about the x-axis, y-axis, and origin.
(a) symmetric about just the x-axis
(b) symmetric about just the y-axis
(c) symmetric about just the origin
(d) symmetric about the x-axis, y-axis, and origin
(e) not symmetric about the x-axis, y-axis, or origin
©Lynch, October 2015
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Math 150, Fall 2015
Exam 2 – Form A
Work Out Problems
Sections 3A-5A
First Name:
Last Name:
Student ID number:
Section Number:
Directions:
1. Show all your work neatly and clearly mark your final answer. You will be graded not only on the final
answer, but also on the quality and correctness of the work leading up to it.
2. No calculators, cell phones, or other electronic devices may be used, and they must all be put away
out of sight.
3. There are 10 problems on this exam worth 5 points each, and a bonus question worth 5 points. You
must show your work to receive credit.
4. Together with the other part of the exam there will be a total of 110 points possible.
5. You may not discuss the contents of the exam with anyone until the exam is returned in class.
THE AGGIE CODE OF HONOR
“On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work.”
Signature:
Note: You are authorized to use a pencil, eraser, and your own TAMU student ID; use of
anything else is a violation of the honor code. If you need any extra paper, please ask your
instructor or TA; do not use your own.
Exam Part
Points Earned
Points
Multiple Choice
50
M.C. Bonus
5
Page 2-3:
20
Page 4-5:
25
Page 6:
10
Exam 1 Grade
100
©Lynch, Octber 2015
Math 150 – Exam 2A
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1. Write the equation of the quadratic function f (x) = 4x2 + 12x + 14 in standard form. Identify the axis
of symmetry for f (x).
Standard Form:
Axis of Symmetry:
2. Find the perpendicular bisector of the line segment between A(−2, −1) and B(4, 7). Write your answer
in slope-intercept form.
Perpendicular Bisector:
©Lynch, Octber 2015
Math 150 – Exam 2A
Page 3 of 6
3. Determine the center and radius for the circle 2x2 + 2y 2 − 3x + 8y − 5 = 0.
Center:
Radius:
4. If g(x) =
(g ◦ f )(x).
3
x2
√
and f (x) = 3 x + 1, calculate and fully simplify (g ◦ f )(x). Also, find the domain of
(g ◦ f )(x) =
Domain of (g ◦ f )(x) in interval notation:
©Lynch, Octber 2015
Math 150 – Exam 2A
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5. Using the graph of f (x) below, graph the function g(x) = 2f (x − 2) − 3. Describe the transformations
used to get g(x) from f (x)
g(x)
f(x)
√
√
6. The function g(x) = − 12 x + 3 + 4 is a transformation of the function f (x) = x. Describe the transformations, in order, to get g(x) from f (x).
1)
2)
3)
4)
7. If (−3, 2) and (5, 6) are endpoints of a diameter of a circle, write the equation for the circle in standard
form.
Equation of Circle in Standard Form:
©Lynch, Octber 2015
Math 150 – Exam 2A
Page 5 of 6
8. An astronaut on Mars throws a potato upward at a velocity of 24 ft/s. If it is released at a point 5 ft
from the ground, its distance s in feet from the ground at t seconds is given by s(t) = −6t2 + 24t + 5.
Find the maximum height the potato reaches, and the time it reaches that height.
Maximum height=
Time when it reaches maximum height: t=
9. Write the formula for the difference quotient and use it to find the difference quotient for f (x) = 2x2 − x.
Fully simplify your answer.
Difference Quotient Formula:
Simplified answer:
©Lynch, Octber 2015
Math 150 – Exam 2A
Page 6 of 6
10. A boat travels at a constant speed for 5 hours upstream on the Mississippi River and travels 25 miles. It
only takes that boat 3 hours to return downstream over those same 25 miles. If the Mississippi is flowing
at a rate of 4 mph, then what would be the boat’s constant speed if it was traveling in still water?
Boat’s Speed in still water:
Bonus Question: Prove f (x) =
√
2x + 4 is a one-to-one function.