Exam

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
 
Determine the intervals on which the function is increasing, decreasing, and constant.
1) 
1) ______
  A)  Increasing on (-∞, 4); Decreasing on (-4, ∞); Constant on (4, ∞)
  B)  Increasing on (4, ∞); Decreasing on (-4, ∞); Constant on (-4, 4)
  C)  Increasing on (4, ∞); Decreasing on (-∞, -4); Constant on (-4, 4)
  D)  Increasing on (-∞, 4); Decreasing on (-∞, -4); Constant on (4, ∞)

Determine the domain and range of the function.
2) 
2) ______
  A)  domain: (-∞, 1]; range: [0, 3]
  B)  domain: [-3, 1]; range: [-3, 0]
  C)  domain: [-3, 0]; range: [-3, 1]
  D)  domain: [0, 3]; range: (-∞, 1]

For the piecewise function, find the specified function value.
3)  f(x) = {table ( (8x + 1, for x < 1,)(5x, for 5 ≤ x ≤ 10,)(5 - 5x, for x > 10) )
f(5) 		3) ______
  A)  25
  B)  -20
  C)  9
  D)  51

For the pair of functions, find the indicated domain.
4)  For f(x) = (square root of (x - 1)/x - 3)
Find the domain of f(x). 		4) ______
  A)  [0, 3) ∪ (3, ∞)
  B)  (1, 3) ∪ (3, ∞)
  C)  [1, 3) ∪ (3, ∞)
  D)  [1, ∞)

Find the average rate of change of the function over the given interval.
5)  y = square root of (2x), [2, 8] 5) ______
  A)  2
  B)  (1/3)
  C)  7
  D)  - (3/10)

6)  Find the intervals where the function is concave up and concave down and the point of inflection
 		6) ______
  A)  up (1, oo) down (-oo, 1) (1,-5)
  B)  up (-oo, 1) down (1, oo) (1,-5)
  C)  up (1,oo) down (-oo, 1) (0, -3)
  D)  up (1,oo) down (-oo, 1) (2, -7)

Solve the problem.
7)  Use the graphs to find the value of (f + g)(3).
 		7) ______
  A)  1
  B)  0
  C)  -1
  D)  3

8)  Use the tables to find (fg)(-8).

column chart ( (x -8 -6 4)(f(x) 7 3 -5 ) ) column chart ( (x -8 2 4)(g(x) -8 2 5 ) )
 		8) ______
  A)  -25
  B)  -56
  C)  6
  D)  64

Determine whether or not the function is one-to-one.
9) 
9) ______
  A)  No
  B)  Yes

10) 
10) ______
  A)  No
  B)  Yes

Decide whether the given functions are inverses.
11) 
two way table ( (x f(x))(45678 1719212325) )​two way table ( (x g(x))(1719212325 45678) )
 11) ______
  A)  No
  B)  Yes

12) 
two way table ( (x f(x))(-2-4-6-8-10 510152025) )​two way table ( (x g(x))(5-10152025 -2-4-6-8-10) )
 12) ______
  A)  Yes
  B)  No

Decide whether or not the functions are inverses of each other.
13) 
13) ______
  A)  No
  B)  Yes

If f is one-to-one, find an equation for its inverse.
14)  f(x) = 7x - 4 14) ______
  A)  f-1(x) = (x - 4/7)
  B)  f-1(x) = (x/7) + 4
  C)  Not a one-to-one function
  D)  f-1(x) = (x + 4/7)

15)  f(x) = square root of (x + 9) , x ≥ -9 15) ______
  A)  f-1(x) = square root of (x - 9)
  B)  f-1(x) = x2 - 9, x ≥ 0
  C)  Not a one-to-one function
  D)  f-1(x) = (x + 9)2

16)  f(x) = (9/x + 8) 16) ______
  A)  f-1(x) = (-8x + 9/x)
  B)  Not a one-to-one function
  C)  f-1(x) = (x/8 + 9x)
  D)  f-1(x) = (8 + 9x/x)