MAT-1221
Problem Set #2
Due 16 NOV 2018
Name:
Instructions:
• Remember that your work is graded holistically, based on the rubric below.
• Show your work. Your work should include enough detail so that one can easily
understand how to work out the problem and find the answer by reading your solution.
• All matrix operations and inverse calculations should be done by hand; you may find
it helpful to check your calculations on a calculator.
• Academic Integrity: It is okay to work together on this, and to seek help from others,
so long as the problem set that you turn in accurately reflects your understanding of
the problems and their solutions.
Mathematics Grading Rubric
5 (100%)
4 (87%)
3 (75%)
2 (60%)
1 (40%) or 0∗ (0%)
Outstanding (“A”)
Good (“B”)
Average (“C”)
Deficient (“D”)
Failing (“F”)
Well-executed,
well-communicated,
essentially correct
Generally
well- Adequately
exe- Flawed
execution Unsatisfactory
executed but may cuted but with possibly with non- execution and/or
have minor com- some non-trivial er- trivial errors or poor communication
munication flaws or rors or inconsistent communication
with fundamental
some math errors
communication
errors
*Note: A blank page, complete nonsense or a haphazard approach (one without a reasonable direction/order)
will earn a zero.
MAT-1221
Problem Set #2
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Due 16 NOV 2018
MAT-1221
Problem Set #2
1
1) Find the domain of the function f (x) = √
.
5+x
Due 16 NOV 2018
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2
2) Let f (x) = x + 2x, and evaluate the following expression.
f (x + h) − f (x)
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MAT-1221
Problem Set #2
3) Describe the
transformations to apply to the graph
√
3
below) to obtain the graph
of f (x) = x (shown
√
3
of g(x) = 3 − x + 2. Then sketch the graph of
g(x) on the axes provided.
Due 16 NOV 2018
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5
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MAT-1221
Problem Set #2
4) Match each equation with the graph of one of the functions f , g, m, or n in the figure.
There isn’t much work to show for this– you need only
indicate your answers. You may indicate your reasons, if you wish (this could help earn more credit for
a wrong answer).
a) y = (x − 3)2 − 4
c) y = −(x − 3)2 + 4
b) y = −(x + 3)2 + 4
d) y = (x + 3)2 − 4
Due 16 NOV 2018
Grade:
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Communication
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MAT-1221
Problem Set #2
Due 16 NOV 2018
5) Consider the quadratic equation 2x2 + 5x − 3 = 0.
a) Solve by factoring.
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b) Solve by completing the square.
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MAT-1221
Problem Set #2
6) Complete the square on the quadratic function
f (x) = 0.5x2 + 4x + 5 to write it in vertex form.
Then find each of the following.
Due 16 NOV 2018
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a) vertex
b) x- and y-intercepts
c) maximum or minimum
d) sketch a graph of the function (a set of axes is provided on the next page)
MAT-1221
Problem Set #2
Due 16 NOV 2018
MAT-1221
Problem Set #2
7) Match each equation with the graph of f , g, h, or k in
the figure.
There isn’t much work to show for this– you need only
indicate your answers. You may indicate your reasons, if you wish (this could help earn more credit for
a wrong answer).
x
c) y = (0.5)x
a) y = 14
b) y = 5x
d) y = 3x
Due 16 NOV 2018
Grade:
5
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MAT-1221
Problem Set #2
8) This exercise illustrates a situation in which the common log is particularly useful, where the natural log is
not. In the scientific community, expressing very large
or very small numbers is done using scientific notation.
A number in scientific notation is written as
Due 16 NOV 2018
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a × 10k
where 1 ≤ a < 10, and k is an integer that corresponds to the magnitude of the number
(the direction and number of spaces one needs to move the decimal place to end up
with the number a, from the original number). Positive exponents correspond to large
numbers, negative exponents correspond to small numbers (less than 1).
For example: 2, 340, 000 = 2.34 × 106 , and 0.0000307 = 3.07 × 10−5 .
Consider the (very large) number 7531 . If you wanted to get an expression of this
number in decimal form, using scientific notation, you might first try plugging it into
your calculator. On the TI-84, this results in an “overflow error”; the number is just
too big for the calculator to handle. We can still accomplish our goal with the use of
the common log!
Start by letting N = 7531 , so that we want to write N in scientific notation, and take
the common log of both sides. Now use properties of logs, along with the LOG function
on the calculator to write N in scientific notation.
MAT-1221
Problem Set #2
Due 16 NOV 2018
9) Suppose that you have $3000 that you can deposit into an account with a 4.2% annual
interest rate. How long will it take for your account to reach $5000 if
a) the account is compounded quarterly?
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b) the account is compounded continuously?
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MAT-1221
Problem Set #2
10) An ordinary annuity pays 6.48% compounded
monthly. A person wants to make equal monthly deposits into the account for 15 years in order to then
make equal monthly withdrawals of $1,500 for the
next 20 years, reducing the balance to zero. How
much should be deposited each month for the first 15
years? What is the total interest earned during this
35-year process?
Due 16 NOV 2018
Grade:
5
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