Key to practice Midterm I

Problem 1

i:  a)  Does not define a function of x.

b)  Not a 1-1 function

c)  Not Applicable

d)  Not Applicable

e)  x:  x = (-y)² + 1 = y² + 1 Yes

y:  -x = y² + 1 No

origin:  -x = (-y)²  + 1 = y² +1 No

ii.  a)  Is a function of x

b)  Not 1-1

c)  Not applicable

d)  Not applicable

e)  x:  No since it is a function.

y:  y = 3(-x)²  - 2  = 3x² - 2 Yes

origin:  -y = 3(-x)²  - 2 = 3x² - 2 No

iii)  a) It is a function

b)  Yes, it is 1-1

c)  y = -2/3 x + 2

d)  -2/3(3 - 3/2 x) + 2 = -2 + x + 2 = x

3 - 3/2(-2/3 x + 2) = 3 + x - 3 =  x

e)  x:  3x + 2(-y) = 6, 3x - 2y = 6, No

y:  3(-x) + 2y = 6, -3x + 2y = 6, No

origin:  3(-x) + 2(-y) = 6, -3x - 2y = 6, 3x + 2y = -6, No

Problem 2

A.  [3(x + h)² + 5(x + h) - 2 - (3x² + 5x - 2)]/h

= [3x²  + 6xh + 3h²  + 5x + 5h - 2 - 3x² - 5x + 2]/h

= [6xh + 3h² + 5h]/h = h(6x + 3h + 5)/h = 6x + 3h + 5

B.  2(3x²  + 5x )³ + (3x² + 5x) = 54x⁶ + 270x⁵ + 450x⁴ + 250x³ + 3x² + 5x

Problem 3

Your explanation here

Problem 4

A.  this is the graph of 1/x shifted 4 to the left and 3 down.

B.  This is the graph of sqrt(x) reflected across the y axis and stretched vertically by a factor of 3.

Problem 5

{x|x not 0 and x >-2}

Problem 6

30 sqrt2 ft/sec or 42.42 ft/sec