MA 15300 Exam 3A Fall 2009 1 Use the functions, () ()21 and 35xfx gx xx+==+−, to answer questions #1 and #2: 1. Find and simplify ()()3fg+. 521213232..... None of the above.ABCDE−−2. Find and simplify ()()fgxD. 222514.52415.527.2261.35. None of the above.xAxxxBxxCxxxDxxE−−+−−+−+++− 3. Which of the following graph best depicts the sign chart given by: ` 3−2 4sign of ()xf −++ +-3 0 2 4 xy -3 0 24xy -3024xy-3 0 2 4xy -302 4 xyA. B. C. D. E.MA 15300 Exam 3A Fall 2009 2 4. Suppose y is directly proportional to the product of w and the square root of x and inversely proportional to the cube of p. If 4, 25, and 2, then 6wx p y== = =. Find y if 7, 4, and 1wx p== =. 12.5168.5121.25.2. Cannot be determined.AyByCyDyE==== 5. Given the function, ()21fxxx=−+, find and simplify ()()fah fah+− ()assume 0h ≠. 222...2.1.2 1hahAhBhCahDhEah−+++−+− 6. Solve the following system of equations for x: 621xyxy=⎧⎨−=⎩ 3.,227.,623.2,27.6,277.,22Ax xBx xCx xDx xEx x=− ==− ==− ==− ==− =MA 15300 Exam 3A Fall 2009 3 Use the graph of ()yfx= given below to answer questions #7 and #8: 7. Find the interval(s) for which f is increasing. [][][][][][].3,1.4,11,5.1,2.4,12,5. No intervals of increasing.ABCDE−−−∪−−−∪ 8. Find the domain, D, and range, R, of ()41yfx=−. [][][] [][] [ ][][].3,6;12,8.3,20;2,8.5,4;12,831.4,5; ,4231.3,6; ,42AD RBD RCD RDD RED R=− =−=− =−=− =−⎡⎤=− =−⎢⎥⎣⎦⎡⎤=− =−⎢⎥⎣⎦ 11xy()4, 1−− ()1, 2− ()2, 3− ()5,1MA 15300 Exam 3A Fall 2009 4 9. Solve the inequality. Express your answer in interval notation. ()()3051xxx−≥++ ()(]()[)()(][)()[).5,1 1,3.5,13,.,51,3.3,.,53,ABCDE−−∪−−−∪ ∞−∞ − ∪ −∞−∞ − ∪ ∞ 10. Given below, on the left, is the graph of a basic function, ()yfx=. The graph on the right was obtained by shifting, reflecting, stretching, and/or compressing the basic graph. Which of the following best describes the graph on the right? 11. Find the standard equation of the parabola whose x-intercepts are 6 and 4− and the highest point has y-coordinate 8. ()()()()()222228.18258.1892.289.418.228Ay xBy xCy xDy xEy x=− + +=− − +=− + +=− + +=− − + ()()()()().3.3.3.3.3Ay fxBy f xCy f xDy fxEy fx=− +=−−=−+=− −=− + x y()3,1−()1, 1− ()4, 3− ()yfx= xy()3, 2− ()1, 4()4,6MA 15300 Exam 3A Fall 2009 5 12. Find the maximum or minimum value of the parabola given by ()242438fx x x=++ and specify whether it is a maximum or minimum value. .3;Maximum.2;Minimum. 3; Minimum.2;Maximum. Not enough information given.ABCDE−− 13. Anthony enters a candy store equipped with $2.10 to buy two kinds of his favorite candy, Gummi bears and jellybeans. Gummi bears sell for $3.00 per pound and jellybeans sell for $2.50 per pound. If he is to buy a total of 0.75 pounds of candy, find the system of equations that would be used to find the amount of each that should be purchased. Let x represent the number of pounds of Gummi bears and y the number of pounds of jellybeans. 2.10.3.00 2.50 0.750.75.3.00 2.50 0.750.75.3.00 2.50 2.102.10.3.00 2.50 2.10. None of the above.xyAxyxyBxyxyCxyxyDxyE+=⎧⎨+=⎩+=⎧⎨+=⎩+=⎧⎨+=⎩+=⎧⎨+=⎩MA 15300 Exam 3A Fall 2009 6 14. Shown below is the apparatus for a zip line (where a person repels down a cable). The two poles are set 75 feet apart. The height of the longer pole is x and the height of the shorter pole is 8 feet. Express the length L of the cable as a function of x. Simplify the function. ()()()()()222. 16 5689. 5625. 5689.75.67ALx x xBLx xCLx xDLx xELx x=−+=+=+=+=+ 15. A tour bus company charges $30 per person up to and including the first 10 people and then $25 per person for each additional person in the group. Find and simplify a piecewise-defined function, C, that specifies the total charge of a tour of x people. ()()()()30 if 0 10.25 if 1030 if 0 10.25 10 if 1030 if 0 10.25 300 if 1030 if 0 10.25 50 ixxACxxxxxBCxxxxxCCxxxxxDCxx<≤⎧⎪=⎨>⎪⎩<≤⎧⎪=⎨+>⎪⎩<≤⎧⎪=⎨+>⎪⎩<≤=+()f 1030 if 0 10.25 550 if 10xxxECxxx⎧⎪⎨>⎪⎩<≤⎧⎪=⎨+>⎪⎩ x 75 8
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