1. An open box is made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. Write the volume of the box as a function of x if the material is 18 inches by 12 inches.
   
   
   a. V(x) = x(12 - 2x)(18 - 2x)   
   b. V(x) = x(12 - x)(18 - x)   
   c. V(x) = 216x
   d. V(x) = 2x(12 - 2x)(18 - 2x)   
   e. V(x) = 2x(12 - x)(18 - x)
   
    
2. A ball is shot vertically upward at a speed of 64 feet per second. The equation that relates the heigh s of the ball as a function of time t is s(t) = 64t - 16t². Determine the height of the ball when t = 1 second.
   a. 0 feet    b. 48 feet    c. 4 feet    d. 80 feet    e. none of these
   
    
3. Find the domain of the function f(x) =
   a. all reals   
   b. all reals except x = 0   
   c. all reals except x = 0, 6
   d. all reals except x = 6   
   e. all reals except x =
    
4. Determine the correct function for the given graph.
   
   
   a. f(x) = x³ + x² - 6   
   b. f(x) = -x³ - x² + 6   
   c. f(x) = x³ + x² - 6x
   d. f(x) = x⁴ + x² - 6   
   e. f(x) = -x⁴ - x² + 6
   
   
    
5. Solve for x:  
   a. x = 2, -5   
   b. x =   
   c. x = 2   
   d. x = -2, 5
   e. x = ,
    
6. The number of bacteria in a culture, where there are initially 200, is given by the formula
   N(t) = 200e^0.1t. Determine the time t it would take for the number of bacteria to double.
   a. 2    b.    c.   
   d. 20    e. 10ln(2)
   
    
7. Find the composite function f(g(x)) when f(x) = 2x + 3 and g(x) = 4x
   a. 6x + 3    b. 8x + 3    c. 8x + 12x    d. 8x² - 3    e. 8x² + 3
   
    
8. A boat is d feet from shore. A person standing on the dock is 60 feet above water level. The angle of depression from the boat to the dock is . Write as a function of d.
   
   a.   
   b.   
   c.
   d.   
   e. none of these
   
    
9. Find all solutions in the interval [0, 2):  
   a. 0, only   
   b. only   
   c. all x   
   d. 0, , , only
   e. none of these
   
    
10. If the range of f(x) = sinx is [-1, 1], what would the range of g(x) = 3sin x + 1 be?
    a. [-3, 3]    b. [0, 2]    c. [-4, 4]    d. [-2, 4]   
    e. none of these
     

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