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Unformatted text preview: NAME Sept. 30, 2002
Teacher Section 2 MATH 115—Exam 1 Write your name, your teacher’s name and your section number on each answer sheet. Answer problem 1 in the
spaces provided on this sheet and each of the remaining numbered problems on a separate answer sheet (see
directions before each problem). In order to receive full credit for a problem you must show appropriate work.
At the end of the exam, place the answer sheets in order and put this sheet on top. No calculators or audio devices are allowed. ,. Answer Problem 1 in the spaces provided below.
(21) 1. Draw the graphs of each of the following on the coordinate axes below. On your graphs label all
intercepts and vertices with their coordinates. Label the axes. a. f(x)=0.5|x+2| b. G(x) =x3 — 8 d. z =—«/T-I_-§ Please turn over for the remaining problems. 2-page 1 of2 Answer Problem 2 on Answer Sheet 2. (10) 2. a. Find the average rate of change of f (x) = from x = 0 to x = 11. Don’t forget to simplify your
answer (h should not a factor of the denominator when you are finished). (5) b. A kennel owner has 300 feet of fencing material to be used to divide a 4x
rectangular area into 10 equal pens, arranged in two rows of five each (see Figure 1). Find a function that models the total area A of the pens .
as a function of the width x of the rectangle. Flgure 1 Answer Problem 3 on Answer Sheet 3. (7) 3. a. Draw the graph for the equation x2 + 25y2 = 100. On your graph label all intercepts and vertices with their coordinates. Label the axes. (10) b. Find all real solutions: x“2 + x1/4 = 6 Answer Problem 4 on Answer Sheet 4. (7) 4. a. Draw a graph of the equation x = ~2y2. On the graph
label all vertices and intercepts with their coordinates.
Label the axes. (10) b. The graph of a function g is shown in Figure 2. Find each of the following. Answers should be in interval
form. i. the domain of g
ii. the range of g
iii. The interval(s) on which g is increasing Answer Problem 5' on Answer Sheet 5. (2)c+5)(x+6)2 (10) 5. Use a table of signs to solve the inequality (9_x) S; 0. Write your solution in interval form. Answer Problem 6 on Answer Sheet 6. . . . . _ (24—3x)3/2
(10) 6. a. Find the domain of the functlon defined by g(x) — — x+2 (11) b. A manufacturer finds that the revenue generated by selling x units of a commodity is given by the
function R(x) = 80x — 0.4x2 (dollars).
i. Draw a graph of R.
ii. Find the number of units that should be manufactured for a maximum revenue from this
iii. How do you know that this number will produce the maximum value for R? . Write the solution in interval form. End of Examination 2-page 2 of 2 """" ”__—__'_'W’__m_”—ﬂ—__— ; ...
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