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hfdg - NAME Oct 30 2002 Teacher Section 4 MATH llS—Exam 2...

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Unformatted text preview: NAME Oct. 30, 2002 Teacher Section 4 MATH llS—Exam 2 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. (7) 1. a. Find g'1(x) if g(x) = 4x7 ~ 8 . How would you prove that your function is the inverse off? (You do not have to carry out the proof.) (8) b. Draw the graph of the equation. 4y2 — 4x2 = 1. On your graph label all intercepts and vertices with their coordinates, show asymptotes (if any) with a dotted line and label any asymptote with an equation. Don't forget to label axes. Please turn over for Problems 2-6. 4———page 1 of 2 Answer Problem 2 on Answer Sheet 2. (10) 2. a. Sketch the graph of the function f(x) = —(x — 2)2(x + 1)2(x + 5) . On your graph label the intercepts with their coordinates or values and show any asymptote with a dotted line and label it with an equation or intercept value. Label the axes. b. In a developing country, one model for the population growth of a city after t years is C(t) = $41.7)” (in thousands). The growth of population in a rural area after t years is modeled by R(t) = 5(0.9)t (in thousands). (a) i. Draw the graphs of C and R on the same coordinate axes. Label graphs clearly with the names of their functions (C, R.). Label intercepts with their values and show clearly any asymptote. (2) ii. What is the meaning of the point of intersection for these models? Answer Problem 3 on Answer Sheet 3. _ 16-x2 (14) 3. Let f(x)l— (x+2)2 . a. Find each of the following for the graph of f. x-intercept(s) y—intercept vertical asymptote(s) horizontal asymptote b. Draw the graph of f Answer Problem 4 on Answer Sheet 4. 4. a. Evaluate each of the following: (12) i. log575—log53 ii. 16'0g27 iii. 1n(%/Z)+1n1 (7) b. Let g(x) = log4(x + 16). (i) Find the domain of g and (ii) draw the graph of g. On your graph show any asymptote with a dotted line labeled with its equation or intercept. Label the intercepts with their coordinates or values. Label axes. Answer Problem 5 on Answer Sheet 5. 5. a. Suppose log 5 = 1.4, log t = -O.3 . Evaluate each of the following. Don't just give a numerical answer; indicate clearly in the steps the log rules you used. (a) i. 104%) ii. log(s t4) (8) b. Write as a single logarithm and simplify: log x ~ 2 log (x 2 + 9) + %log (8) Answer Problem 6 on Answer Sheet 6. 6. Find all real solutions to the equations: (8) a. 4(1+ 3"”) = 24 (8) b. l—3ln(8+x)=0 End of Examination 4-page 2 of 2 ...
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