Download Exam Name___________________________________ SHORT

Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
2x - 4
1) Simplify:
6 - 3x
2) Simplify:
1)
64x 3 2/3
27
2)
3) Simplify and express your answer in terms of positive exponents: (2x-3 y2 )5
4) Simplify and express your answer in terms of positive exponents:
x -3y -2
x 2y -7
3)
4)
5) Simplify and express your answer in terms of positive exponents:
5
32x -10y 15
5)
6) Multiply and simplify: (x + 1)(x + 4)
6)
7) Multiply and simplify: (x 3 - 9)(x3 + 9)
7)
8) Simplify: 7 2a2 (a + b) - 8b(a - b)
8)
9) Simplify: ( a2 + b2 - a)( a2 + b2 + a)
9)
10) Completely factor: x 2 - 10x + 16
10)
11) Completely factor: 2x2 - 8
11)
12) Perform the operation and simplify your answer:
13)
Perform the operation and simplify your answer:
14) Rationalize the denominator:
x+7
6
·
x
3x + 21
2x - 2y
3z
12)
13)
x-y
6z 3
1
3- 2
14)
1
15) Rationalize the denominator and simplify:
2+
2-
x
x
15)
16) Solve: x = 2x - (6 - x)
16)
17) Solve: (x + 1)2 - 2x = x 2 + 2
17)
18) A garage door company's total monthly revenue from the sale of x garage doors is given by
R = 925x and its total monthly costs are given by c = 575x + 2100. How many garage doors
need to be sold each month to break even? In other words, when will revenue equal costs?
18)
19) Solve:
2x - 3
=3
x
20) Solve:
1 + 3x =
19)
2x + 6
20)
21) Solve: x 2 = 5x
21)
22) Solve: 3x 2 + x - 2 = 0
22)
23) Suppose the weekly revenue for a company is given by r = -2p 2 + 400p where p is the price
of their product. What is the price of their product if the weekly revenue is $18,750?
23)
24) Solve: 5x - 2
24)
14 - 3x
25) A manufacturer has 4000 units of product x in stock and is now selling it at $10 per unit.
Next month the unit price will increase by $2. The manufacturer wants the total revenue
received from the sale of the 4000 units to be no less than $45,000. What is the maximum
number of units that can be sold this month?
25)
26) Solve: 4x - 3 = 7
26)
27) Solve: x - 6
27)
6
28) Solve: 5 - 2x > 3
28)
29) Find the domain of the function: f(x) =
x - 11
29)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
30) The domain of the function f(x) =
A) all real numbers
x+2
x 2 - 16
is
30)
2
B) all real numbers except 4 and -4
2
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
31) If f(x) = x 2 and g(x) = 2x + 1, find:
(a) (f + g)(x)
(b) (f + g)(3)
(c) (f - g)(x)
(d) (fg)(x)
1
(e) (fg) 2
(f)
31)
f
(t2 )
g
(g) f(g(x))
(h) f(g(1))
(i) g(f(x))
32) If f(x) =
x + 1 and g(x) = 3x2 + 4, find f(g(x)).
32)
33) The graph of y = f(x) is shown below. (a) What is the domain of f? (b) What is the range of
f?
33)
34) Suppose the weekly demand function for a pound of the house blend coffee at a local
q
coffee shop is p = 15 .
60
34)
(a) If the current price is $11.25 per pound, how much coffee is sold each week?
(b) If they are selling 180 pounds of coffee each week, what is the current price?
(c) If the owner wants to sell 300 pounds of coffee each week, what should the price be?
35) Suppose the yearly demand function for an artist's paintings is p =
25,000
.
q
35)
(a) If the current prices is $200.00 per painting, how many paintings are sold each year?
(b) If the artist wants to sell 4 paintings per year, what should the price be?
36) Suppose the weekly supply function for a large pizza at a local pizza parlor is p =
(a) How many large pizzas will be supplied if the price is $12.50 per pizza?
(b) How many large pizzas will be supplied if the price is $18.75 per pizza?
(c) How does the amount supplied change as the price increases?
3
q
.
40
36)
2
37) If g(x) = x - 2x + 1,
2 - 3x,
(a) g(-3)
(b) g(0)
(c) g(4)
38) If f(x) =
if
if
x < 0,
x 0
37)
x + 4 and g(x) = x 3 + 5, find: (a) f(g(x)) and (b) g(f(x)).
39) h(x) = x 3 - 7x 2 + 1; g(x) = x2 + 2x. Find
(a) (h + g)(.1)
(b) (h - g)(.1)
(c) (hg)(.1)
h
(d)
(.1)
g
38)
39)
4