Answers To Sample Test
 1)  Domain -- x < 4
      Range -- y > 0
      Zero at ( 4, 0)
 
2)  Domain -- all real numbers but 2/3
     Range -- all real numbers but 5/3
     Zero at ( 0, 0)
 
3)  Range is all real numbers
     zeros at (-4, 0), (-1, 0), and (1, 0)

4)  a)  5x + 5
     b)  -2x
     c) 4(x + 5)2
     d)  (2x + 5)2
     e)  4/x, x can't equal 0
     f)  g[f(7)] = g(28) = 784

5)             a)                                             b)                                    c)
 
  

6)
 
x y y = x origin
a) no no no yes
b) yes yes no yes
c) no yes no no
      
7)  It is symmetric to the x-axis

8)  a) is a vertical stretch and translation of 1 right and 5 up
     b)  is a reflection about the x-axis and a translation of 1 left and 3 down
  

9)    To prove this you must show both ways!!
    f[g(x)] = f(2x-1) = (2x - 1 + 1)/2 = 2x/2 = x
 
    g[f(x)] = g[(x + 1)/2] = [2(x + 1)/2] - 1 = x + 1 - 1 = x

10)  To find the rule interchange x and y and solve for y.
            x = y2 - 2
            x + 2 = y2
         _____
            y = - \/ x + 2   , x > -2

11)                                          a)                                                                      b)
 
  

12)    a)  A(b, h) = bh/2
          b)  A(2, 3) = (2)(3)/2 = 3   and A(5, 6) = (5)(6)/2 = 15
          c)  5 = bh/2  ==>    10 = bh ==>  h = 10/b

13)  a)  4
        b)  1, 0, -1, 0
        c)  -1, 1, 0, 1
        d)  Changes amplitude but not period length.
 
        e)  Changes period length to 2 (horizontal shrink)  but does not change amplitude
 
        f)  Reflection about the x-axis
 
        g)  Reflection about the y-axis


Hope you did well on this opportunity.  If not go back and study the previous sections until you have mastered the material.  Especially study the reflections, stretches and shrinks, and of course, the translations.  Good luck!!