Quiz 3 Chapter 2 Sections 4 - 6

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1)Write as a product of linear factors: f(x) = x4- 5x3 + 8x2 - 20x + 16.

(a) (x + 2)(x - 2)(x - 4)(x - 1)
(b) (x + 4)(x + 1)(x - 2i)(x + 2i)
(c) (x - 4)(x - 1)(x + 2i)(x - 2i)
(d) (x + 4)(x + 1)(x + 2i)(x + 2i)
(e) None of these


2) Use the fact that 3i is a zero of f(x) to find the remaining zeros:

f(x) = x4 - 6x3+ 14x2 - 54x + 45.

(a) 0, -3i
(b) -1, -5, -3i
(c) 2, 3, -3i

(d) 1, 5, -3i
(e) None of these


3) If 2i and 3 + sqrt(5) are roots of a rational coefficient fourth degree polynomial what are the other roots?

(a) -2i only
(b) -2i and 5 - sqrt (3)
(c) -2i and 3 - sqrt(5)
(d) 3 - sqrt(5)


4) [Image]

Determine the horizontal asymptote of the graph above

(a) y = -1
(b) y = 1
(c) x = -1
(d) x = 1
(e) None of these


5) Find the vertical asymptote:

                   7
f(x) =         ---------
                 x +  2

  (a) x = -2 (b) y = -2   (c) (0, -2)   (d) y = 0 (e) None of these


6)

.                                            x + 3
.Find the vertical asymptote(s): f(x) =________________
                                        (x - 2)(x + 5)

a)  y = 2, y = -5, y = -3         (b)  x = 2, x = -5, x = -3, x = 1
 (c)  x = 1                         (d)  x = 2, x = -5
 (e)  None of these

7)

.                                           x2 - 1
.Find the horizontal asymptote(s): f(x) = _______
                                            x2 + 9 

(a) y = 1 (b) y = 0 (c) x = 1 (d) x = plus or minus 1 (e) None of these


8)
                         x3 + 1
 Find the domain: f(x) = ________
                         x2 + 4       

(a) All reals (b) All reals except x = -2 (c) All reals except x = -1 (d) All reals except x = -2, -1 (e) None of these


9)

.                                                        25,000
.Suppose the cost C of removing p% of pollutants is C =_________ 0 < p <100
                                                        100 - p
   100.  Find the cost of removing 90%.

(a)  $225,000          (b)  $2778              (c)  $2      
 (d)  $2250             (e)  None of these

10).

						x2+ 3x + 1
.Find the horizontal or slant asymptote: f(x) =_____________
                                                   x + 1 

a) x = -1 (b) y = x + 3 (c) y = x + 2 (d) y = 0 (e) None of these


11)[Image]
    							    
Match the rational function with the correct graph above: f(x) =   X + 6 
                                                                   x + 2




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