Math 117
Fall 2015
Exam 1 Tactics
DATE AND TIME
Friday, 02 October 2015
11:00 – 11:50pm
352 Zumberge Hall

WHAT TO DO ON TEST DAY
• Plan to get to class early! Extra time will not be given to those who show up late.
• Also, plan to use the restroom or any other activity before the exam. The exam is only 50 minutes long. Once exam starts, you may not leave the room unless you first turn in your test, and then you may not return.
• Regardless of what you may have experienced during your quizzes or homeworks, we take security and academic honesty very seriously during exams.
• You should bring pens/pencils and erasers only. No calculators, no cheat sheets. If you need extra scratch paper during the exam, just ask. If you have a bag, make sure it is well under your seat.
• All phones that you do have must be turned completely off. Vibrate = Off !
• Do not reach into your purse, backpack, or pockets. You will have to turn in your exam immediately if you do.
• The exam will end very promptly after 50 minutes. There are other classes use our room before and after us, and we can’t disrupt their schedule with our exam.
HOW TO PREPARE
• All of the questions will come from the list in this document, with the specific numbers and/or details changed. In addition to the homework and quiz questions, you should know how to do as many of these as possible.
• Practice writing up these problems on paper, to the point that you can do similar problems on your own, without the aid of the textbook or a calculator.
• Practice even the problems that you already know how to do well. You must be able to do them quickly (the exam is timed), while still providing a careful solution that shows every step, explaining clearly to the reader what you’re doing and why you’re doing it.
• You will be graded less on your final answer to a problem, and more on your ability to construct a legible and coherent explanation of how you got to that answer. This is an exam: do not do work in your head, and do not skip steps.

WHAT WILL BE ON THE EXAM
The first exam will consist of 8 questions. The distribution of points will be indicated in the exam. These questions will cover material from Sections 2.1 – 2.8 and Section 3.1 of your textbook. Specifically, you are expected to be able to answer the following questions.
Questions from our textbook have their numbers listed in blue.
1. (2.1.28) Determine whether the three points are collinear:
(−1, −3),

(−5, 12),

(1, −11)

2. Find the points that that divide the line segment connecting (1, −2) and (4, −1) into four equal parts.
3. (2.2.24) Decide whether or not the equation has a circle as its graph. If it does, give the center and radius. If it does not, describe the graph.
9x2 + 9y 2 + 12x − 18y − 23 = 0
4. (2.2.49) Find the coordinates of all points whose distance from (0, 1) is
√
distance from (5, 4) is 10.

√

10 and whose

5. (2.2.50) Find the equation of the circle of least radius that contains the points (1, 4) and (−3, 2) within or on its boundary.
6. (2.3.2/4/6) Determine whether each relation determines a function:
(a)

(8, 0), (5, 7), (9, 3), (3, 8)

(b)

(9, −2), (−3, 5), (9, 1)

(c)

(−12, 5), (−10, 3), (8, 3)

7. Determine whether each equation defines y as a function of x:
(a)
(b)
(c)
(d)

y = |x| + 5
−x + y 2 = 2
√
y= 3x x = |y| + 5

8. Decide whether or not each of the equations in the last question is symmetric with respect the x-axis, the y-axis, or the origin.
9. Determine the domain of the following function: f (x) =

x+7
√
4− 1−x

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10. Write the equation 2x − 5y = −15 in slope-intercept form. Find any x-intercepts and y-intercepts of its graph.
11. (2.5.53) Find k so that the line through (4, 1) and (k, 2) is
(a) parallel to 3y + 2x = 6
(b) perpendicular to 2y − 5x = 1
12. (2.5.59) When the Celsius temperature is 0◦ the corresponding Fahrenheit temperature is 32◦ . When the Celsius temperature is 100◦ the corresponding Fahrenheit temperature is 212◦ . Let C represent the Celsius temperature and F represent the
Fahrenheit temperature.
(a) Express F as an exact linear function of C.
(b) Solve the equation in part (a) for C, thus expressing C as a function of F .
(c) For what temperature is F = C a true statement?

13. Find the value of a in the domain of f (x) =

2x
+ 2 for which f (a) = 4.
3

14. Graph the following function, and find all x-intercepts and y-intercepts:

 −x2 + 4, for x ∈ (−∞, 1)

−x + 2, for x ∈ [−1, 1] f (x) =


3x − 2, for x ∈ (1, ∞)

15. (2.7.47) Determine whether the following function is even, odd, or neither. f (x) = x3 − x + 9

16. Consider the equation y = 3x3 + 2x2 − 5.
Make each of the following graph transformations, using this same equation as a starting point for each part. You do not need to simplify the resulting equations.
(a) Shift the graph down by 5 units.
(b) Shift the graph left by 3 units.
(c) Reflect the graph across the y-axis.
(d) Scale (stretches) the graph horizontally by a factor of 2.
(e) Scale (stretches) the graph vertically by a factor of 4.

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17. For each of the following, write and simplify the difference quotient

f (x+h)−f (x)
:
h

(a) f (x) = 4x2 + 7x + 1
2
(b) f (x) =
1+x
18. (2.8.14) For the following pair of functions, find (f + g)(x), (f − g)(x), (f g)(x), and
(f /g)(x). Give the domain of each. f (x) =

√

5x − 4,

g(x) = −

1 x √
19. (2.R.21/22) Let f (x) = x + 1 and g(x) = 2x−7. Find both (f ◦g)(x) and (g ◦f )(x), and give the domain of each.
20. (3.1.24) Let f (x) = −3x2 + 24x − 46. Complete the square to put the function in the form f (x) = a(x − h)2 + k. Use this to determine the following:
(a) the vertex of the parabola
(b) its axis of symmetry
(c) the domain and range of f (x)
(d) the intervals on which f (x) is increasing/decreasing
21. (3.1.51) The number of mosquitos, M (x), in millions, in a certain area of Florida depends on the June rainfall, x, in inches. The function
M (x) = 10x − x2 models this phenomenon. Find the amount of rainfall that will maximize the number of mosquitos. What is the maximum number of mosquitos?

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