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Quiz 2.5 - 2.6 Name___________________________________ Score ______________ Find the requested value. 1) 1) 6x + 4 if x ≤ 0 f(5) for f(x) = 6 - 4x if 0 < x < 4 x if x ≥ 4 Graph the function. 2) 2) 10x + 2 2x2 - 5 f(x) = if x < 0 if x ≥ 0 y 10 5 -10 -5 5 10 x -5 -10 Give a formula for a piecewise-defined function f for the graph shown. 3) 3) 6 y 4 2 -6 -4 -2 2 4 6 x -2 -4 -6 01/25/2008 Graph the equation. 4) y = x - 1 4) y x Solve the problem. 5) A video rental company charges $5 per day for renting a video tape, and then $4 per day after the first. Use the greatest integer function and write an expression for renting a video tape for x days. 6) Sketch a graph that depicts the amount of water in a 50-gallon tank during the course of the described pumping operations. The tank is initially full, and then a pump is used to take water out of the tank at a rate of 4 gallons per minute. The pump is turned off after 5 minutes. At that point, the pump is changed to one that will pump water into the tank. The change takes 2 minutes and the water level is unchanged during the switch. Then, water is pumped into the tank at a rate of 2 gallons per minute for 3 minutes. 5) 6) gallons minutes 7) Find f (-3) when f(x) = 4x - 6 and g(x) = 3x2 + 14x + 4. g 2 7) Perform the requested operation or operations. 8) f(x) = 7 - 6x, g(x) = -2x + 6 Find (f + g)(x). 9) f(x) = 8x - 2, g(x) = 3x + 3 Find (fg)(x). 9) 10) f(x) = 4x + 6, g(x) = 4x - 1 Find (f ∘ g)(x). 11) f(x) = 8) 10) x-2 , g(x) = 7x + 2 7 11) Find (g ∘ f)(x). Find the specified domain. 12) For f(x) = 2x - 5 and g(x) = x + 5, what is the domain of f ∘ g? 13) For f(x) = x2 - 25 and g(x) = 2x + 3, what is the domain of f/g? 3 12) 13) For the functions f and g, find the requested value. 14) Use the graphs of f and g to find f(3) - g(3). 5 y 5 5x -5 5x -5 -5 -5 y = f(x) 15) Use y = g(x) the graphs of f and g to find (g ∘ f)(-2). 5 -5 14) y -4 -3 -2 15) y 5 4 4 3 3 2 2 1 1 -1 1 2 3 4 5 x -5 -4 -3 -2 -1 1 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 y = f(x) y 2 3 4 5 x y = g(x) Solve the problem. 16) Regrind, Inc. regrinds used typewriter platens. The cost to buy back each used platen is $2.10. The fixed cost to run the grinding machine is $114 per day. If the company sells the reground platens for $5.10, how many must be reground daily to break even? 4 16)