Key to Practice Midterm I

Problem 1

1.  

   1. No, since an ellipse does not satisfy the VLT
      

   2. Not a Function
      

   3. NA
      

   4. NA
      

   5. Symmetric about the x-axis, y-axis, and the origin
      

2.  

   1. Yes
      

   2. 1-1
      

   3. f^-1(x) = [(x + 3)/2]^1/3
      

   4. 2[((x+3)/2)^1/3]³ - 3 = 2(x + 3)/2 - 3 = x + 3 - 3
      [((2x³ - 3) + 3)/2]^1/3 = (2x³/2)^1/3 = (x³)^1/3 = x
      

   5. No Symmetry
      

Problem 2

1. [(x + h)² - 7(x + h) - 1 - (x² - 7x - 1)]/h 
   = [x² + 2xh + h² - 7x - 7h - 1 - x² + 7x + 1]/h
   = [2xh + h² - 7h]/h
   = h(2x + h - 70/h = 2x + h - 7
   

2. 9x² - 21x - 1
   

3. -11
   

4. -10
   

Problem 3

580 skiers

Problem 4

1. up 3 left 4
   

Problem 5

Not a right triangle

Problem 6

520 species