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Purdue MA 15300 - Exam 3A

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MA 153 Exam 3A Spring 2007 .Use the functions and ()xxxf 32−=()5−=xxg to answer questions #1 and #2: 1. Find and simplify . ()(2fg−−)) . 17. 5.17. 13. None of the aboveABCDE− 2. Find and simplify ()(xgf D 52.53.403.158.4013.2232232−−−−+−+−+−xxExxxDxxCxxxBxxA 3. Which of the following sign charts describes the graph of the function ()xfy= given below. x y ()xfy = -5 0 4 6 5−4 65−4 6+ _ + sign of ()xfB. A. +++−sign of ()xf_ 5−4 6_ + + sign of ()xf_ C. 5−4 6_ _ + + sign of ()xf D. 5−4 6_ _ + sign of ()xf_ E. 1MA 153 Exam 3A Spring 2007 )4. If the point is on the graph of (2,3P −()yfx=, find the corresponding point on the graph of . ()41yfx=+()()1.,421.,22.8,4.8,2. None of the above.ABCDE⎛⎞−⎜⎟⎝⎠⎛⎞−⎜⎟⎝⎠−− 5. Solve the following system of equations for y. 222255xyxy⎧+=⎪⎨−=⎪⎩ .0,3.0,4.4,.3,.5,Ay yBy yCy yDy yEy y=====− ==− ==− =534 6. Suppose y is directly proportional to the square root of x and inversely proportional to the product of v and w. If x=36, v=2 and w=1, then y=9. Find the constant of proportionality, k. above theof None .2.21.3 .31 .EkDkCkBkA==== 2MA 153 Exam 3A Spring 2007 ]]Use the graph of a function given below to answer questions #7 and #8. ()xfy = xyy=fx()()0,2−()3,1− ()0,0 ()0,2 ()3,1− 7. Find the interval(s) for which f is increasing. Express your answer in interval notation. [][[][[][][][]2,2.2,10,2.1,1.1,01,2.2,11,2 .−∪−−∪−−∪−−EDCBA 8. Choose the graph that depicts the graph of (231+= xfy). yxy xyB. A. xC. 1 11 1 11 xyxyD. E. 1 111 3MA 153 Exam 3A Spring 2007 9. Find a linear function such that ()15f= and ()29f=. . 4 191. 54. 4 111. 44. None of the above.Ay xBy xCy xDy xE=−=+=+=− 10. Find the standard equation of the parabola with vertical axis whose vertex is and passes through the point . (1,2 −−V)()5,4− ()()()()()1223.12493 .1261 .1235 .1271 .22222−+=−+−=−−=−+=−−=xyExyDxyCxyBxyA 11. Solve the following inequality. Express your answer in interval notation. ()()()231xxx−+−≤0 (][)[][)(][ ][].,32,.3,12,.,31,2.1,2. None of the aboveABCDE−∞ − ∪ ∞−∪∞−∞ − ∪ 4MA 153 Exam 3A Spring 2007 12. Express the parabola in standard form. ()1822−−= xxxf()()()()2222.2415. 2 2 9. 2 2 7.2417. None of the above.Ay xBy xCy xDy xE=−+=−−=−+=−− 13. A farmer has 3000 feet of fence to enclose a rectangular field and subdivide it into three rectangular plots (see the figure). If x denotes the width of the field and y the length, find the value of x so that the total area of the field is maximized. y x .250 feet. 750 feet. 1000 feet. 375 feet. Not enough information given.AxBxCxDxE==== 14. A helicopter lifts off the ground vertically at a rate of 6 meters/second. A person is standing at a point 75 meters away due west of the point at which the helicopter took off. If t denotes the time (in seconds) since the helicopter lifted off, express the distance, d, between the helicopter and the person as a function of t. Simplify the function. ()()()()()222. 6 75. d t 6 75. 6 5625. 36 5625. 36 5625Adt tBtCdt tDdt tEdt t=+=+=+=+=+ 5MA 153 Exam 3A Spring 2007 15. A tour bus company charges fares based on the number of people in a group. For one particular trip, the company charges $30 per person for a group of 25 people or less. For each additional person above 25, the company charges $28 per person. Let C be the total charge for the trip and x the number of people. Express C as a function of x. Simplify the function. ()()()()()30 if 25.28 50 if 2530 if 25.58 if 2530 if 25.28 if 2530 if 25. 28 750 if 2530 if 25. 58 25 if 25xxACxxxxxBCxxxxxCCxxxxxDCxxxxxECxxx≤⎧⎪=⎨+>⎪⎩≤⎧⎪=⎨>⎪⎩≤⎧⎪=⎨>⎪⎩≤⎧⎪=⎨+>⎪⎩≤⎧⎪=⎨−>⎪⎩


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Purdue MA 15300 - Exam 3A

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