MA 153 Exam 3A Fall 200311. Given the function † g x( )=3 + x2 - x, find and simplify † g1aÊ Ë Á ˆ ¯ ˜ .† A. 3 + a2 - aB. 2a -13a + 1C. 3a + 12a -1D. 3a + 1( )2a -1( )a2E. 2 - a3 + aUse the graph of the function † y = f x( ), shown below, to answer questions #2 and #3:2. Find the domain, † D, and the range, † R, for the function † y = f 3x( ).† A. D = -23,43È Î Í ˘ ˚ ˙ ; R = -3,5[ ]B. D = -2,4[ ]; R = -9,15[ ]C. D = -6,12[ ]; R = -3,5[ ]D. D = -2,4[ ]; R = -1,53È Î Í ˘ ˚ ˙ E. None of the above3. Find the domain, † D, of the inverse function, † y = f-1x( ).† A. D = -4,2[ ]B. D = -3,5[ ]C. D = -12,2È Î Í ˘ ˚ ˙ D. D = -5,3[ ]E. Cannot be determinedxy† -2,5( )† 4,-3( )† 0,0( )† y = f x( )MA 153 Exam 3A Fall 200324. Solve the system:† 2x + 3y = 118x +12y = 20Ï Ì Ó † A. 0,113Ê Ë Á ˆ ¯ ˜ B. 9,-73Ê Ë Á ˆ ¯ ˜ C. 52,0Ê Ë Á ˆ ¯ ˜ D. There is no solution.E. All ordered pairs x, y( ) such that 2x + 3y = 11.5. Given below is the sign chart for a function. Which of the following could be the graph of thefunction?† -5† -1† 3† 0sign of † f x( )† -† -† +† +† +A.† x† y-5-130B.† x† y-5-130C.† x† y-5-130D.† x† y-5-130E.† x† y-5-130MA 153 Exam 3A Fall 200336. Assume † y is directly proportional to the sum of † x and the square root of † w and inverselyproportional to † r. If † x = 4, w = 36, and r = 2, then y = 7. Find † y if † x = 8, w = 9, and r = 4.† A. y = 2.75B. y = 3.85C. y = 4.75D. y = 1.62E. None of the above7. Explain how the graph of the function † y = - f x + 5( ) compares to the graph of † y = f x( ).8. Given † f x( )=43x + 5 and † g x( )= 3x + 1, find and simplify † g o f( )-2( ).† A. -11B. 20C. -25D. -43E. None of the above9. Find the intervals for which the graph of † y = 4 x +1( )2- 3 is increasing.† A. 1,•[ )B. -1,•[ )C. -•,1( ]D. -•,-1( ]E. None of the aboveA. Reflect the graph of † y = f x( ) throughthe † x -axis and shift right 5.B. Reflect the graph of † y = f x( ) throughthe † y -axis and shift left 5.C. Reflect the graph of † y = f x( ) throughthe † x -axis and shift left 5.D. Reflect the graph of † y = f x( ) throughthe † y -axis and shift right 5.E. None of the aboveMA 153 Exam 3A Fall 2003410. Given the function † f x( )= 5 - 2x2 for x £ 0, find the inverse function, † f-1.† A. f-1x( )=15 - 2x2B. f-1x( )= -5 - x2C. f-1x( )=x - 54D. f-1x( )= -x - 52E. f-1x( )=5 - x411. Given below is the graph of a piecewise-defined function. Choose the function that corresponds tothis graph.† A. f x( )=-1 if x < 1x2- 3 if x ≥1Ï Ì Ô Ó Ô B. f x( )=1 if x < -13 - x2 if x ≥ -1Ï Ì Ô Ó Ô C. f x( )=-1 if x £ 1x2- 3 if x >1Ï Ì Ô Ó Ô D. f x( )=1 if x £ -1x2- 3 if x > -1Ï Ì Ô Ó Ô E. f x( )=1 if x < -1x2- 3 if x ≥ -1Ï Ì Ô Ó Ô 12. Solve the following inequality. Express your answer in interval notation.† x + 1( )x - 3( )2x + 4( )> 0† A. -1, 3( )» 3,•( )B. -4,-1( )» 3,•( )C. -•,-4( )» -4,-1( )D. -•,-4( )» -1,3( )» 3,•( )E. -4,-1( )» 3,•( )xy† 1323412MA 153 Exam 3A Fall 2003513. An apartment manager has found that 45 units of his building are occupied when the rent is $520per month. However, when the rent is lowered to $480 per month, the number occupied is 53units. If the number of occupied units, † N, is linearly related to the rent charged, † r, express † N interms of † r.† A. N = -15r + 529B. N = -5r + 295C. N = -15r + 59D. N = -5r + 745E. N = -15r +14914. During a recent baseball game, a batter popped up a pitch into the shallow outfield. The path theball took was in the shape of a parabola. The ball was not caught and landed on the ground after 4seconds. Let † y = the height of the ball in feet and † x = time in seconds. If the maximum heightthe ball reached was 120 feet, find a standard equation for the path of the ball. Disregard theheight of the batter. † A. y = -7.5 x - 4( )2+ 120B. y = -30 x - 2( )2+ 120C. y = -x2+ 120D. y = -7.5 x + 4( )2+ 120E. y = -30 x + 2( )2+ 12015. A farmer is to build 5 rectangular pens of equal size with openings as shown in the figure. Eachopening is 6 feet wide and the total area is to be 3000 square feet. If † x represents the total lengthand † y the width, express the amount of fencing needed, † F, as a function of † x. Simplify thefunction.† A. F x( )= 2x +18,000x- 30B. F x( )= x1,515 - x3Ê Ë Á ˆ ¯ ˜ C. F x( )= x +18,000x- 36D. F x( )= x315 - x3Ê Ë Á ˆ ¯ ˜ E. F x( )= x +3,600x- 36† x†
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