MA 153 Exam 3A Spring 2008 Use the functions, ()23fxx=+x and ()1gxx= to answer questions #1 and 2: 1. Find and simplify . ()(4fg+−)5.49.415.417.4. None of the above.ABCDE−− 2. Find and simplify ()()fgxD . 22232.31.3.313.1.3AxBxxxCxxxDxExx+++++ 3. Given below is the graph of the function, y=f(x). Find all values of x such that . ()0fx> y ()( )()(()(()()()().1,5 5,.,4 4,.,45,.4,1 1,5.4,1 5,ABCDE∪∞−∞ − ∪ −−∞ − ∪ ∞−∪−∪∞))1x - 4 y=f(x) 5 1 1MA 153 Exam 3A Spring 2008 4. Let y=f(x) be a function with domain, []2,5D =− and range, []6,3R =− . Find the domain and range for . ()23yfx=+ [][] [[]][] [ ]3.1,8; 3,2.5,2;123.5,2; 3,2.1,8; 12,6. None of the above.AD RBD RCD RDD RE,6⎡⎤==−⎢⎥⎣⎦=− =−⎡⎤=− =−⎢⎥⎣⎦==− 5. Choose the correct graph that depicts ()22if 14if 1xxfxxx+≤−⎧⎪=⎨−>−⎪⎩ y A. y1 1 y1 1 B. y1 1 E. 1 1 C. yD. 1 1 2MA 153 Exam 3A Spring 2008 423232424Use the parabola, , to answer questions #6 and #7: ()222fx x x=−− 6. Express the parabola in standard form. () ( )() ( )() ( )() ( )2222.1.2.1.2. None of the above.Afx xBfx xCfx xDfx xE=+ −=−−=+ −=−− 7. Find the zero(s) and the minimum value of the parabola. . zeros: 4,6; min value 25. zeros: 6,4; min value 24. zeros: 4,6; min value 23. zeros: 6,4; min value 25. None of the above.AxBxCxDxE=− =−=− =−=− =−=− =− 8. Several values of two functions F and G are listed in the following tables: x 8 5 3 1 F(x) -2 6 Find ()(5GFD)8 .7.6.9.3.1ABCDE−− 4 9 x 2 4 5 6 G(x)-5 7 1 -3 3MA 153 Exam 3A Spring 2008 9. If ()32238fxx kx xk=− +−, find k such that the graph of f contains the point (). 1,16−.5.2.5.2one of the a==−=−=. N bove.AkBkCkDkE10. Solve the inequality. Express the answer in interval notation. 23025xx+<− ()()()()()(()().,55,.5,3 3,5.,5 3,5.5,3 5,. None of the above.ABCDE−∞ − ∪ ∞−− ∪−−∞ − ∪ −−− ∪ ∞)11. Solve the following system of equations for x. 222110xyxy+=⎧⎪⎨+=⎪⎩.1,333.,55.3,99.1,5. None of the above.Ax xBx xCx xDx xE=− ==− ====− = 12. Which of the following is true about the system of equations given by: 36931xyxy+=⎧⎪⎨+=⎪⎩8. The solution is in .. The solution is in .. The solution is in .. There is no solution.. There are infinitely many solutions.AQIIBQIIICQIVDE 4MA 153 Exam 3A Spring 2008 5 13. The price of admission to a school play was $4.00 for students and $6.00 for nonstudents. If 625 tickets were sold for a total of $2800.00, how many student tickets were purchased? Choose the answer that best describes the solution. . At least 200, but less than 300.. At least 300, but less than 400.. At least 400, but less than 500.. At least 500, but less than 600.. Not eoungh information given.ABCDE 14. A section of a suspension bridge is in the shape of a parabola (shown below). The supports on either end are 100 yards apart and rise 40 yards off the ground. The lowest point of the suspension cable is 10 yards off the ground. Find the standard equation for this parabola. y ()()()()()222223.502503. 100 1010001.502501. 100 1010001.10510Ay xBy xCy xDy xEy x=−+=−+=−+=−+=−+10100 15. The ideal gas law states that the volume, V, that a gas occupies is directly proportional to the product of the number, n, of moles of gas and the temperature, T, and is inversely proportional to the pressure, P. If , then 1.5, 400, and 202nT P== =25V=. Find the constant of proportionality, k. Round your answer to the nearest tenth. .0.2.8.4. 74.3. 12.6. None of the above.AkBkCkDkE==== x
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