44 Find the zeros of f (x), and state the multiplicity of each zero.
a.
b.
c.
d.
e.
f.
g.
x = 3 , multiplicity 2
x = 0 , multiplicity 1
x = 3 , multiplicity 4
x = 0 , multiplicity = 2
41 Find a polynomial f (x) of degree 3 that has the indicated zeros and satisfies the given
condition.
4, - 1, 3 ; f ( 0 ) = 36
a.
b.
c.
d.
50 A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zeros
and degree. Express f ( x ) as a product of linear and quadratic polynomials with real
coefficients that are irreducible over R.
5 , - 4 - 3 i ; degree 3
a.
b.
c.
d.
55 Sketch the graph of f.
a.
b.
c.
59 Determine the domain of f- 1 for the function without actually finding f- 1. Hint: First
find the domain and range of f.
a.
b.
c.
66
Solve the equation.
x=2
a.
x=3
b.
x=4
c.
x=-2
d.
69 Solve the equation. log 2 (x - 4) = 3
a.
12
b.
18
c.
10
d.
7
70 Express in terms of logarithms of x, y. log 7 ( xy )
log 7 ( x ) - log 7 ( y )
a.
log 7 ( x ) + log 7 ( y )
b.
log 6 ( x ) + log 6 ( y )
c.
ln ( x ) + ln ( y )
d.
73 Write the expression as one logarithm. log 3 ( 7 z ) - log 3 ( x )
a.
b.
c.
d.
77 Solve the equation. log 5 ( x + 7 ) + log 5 ( x +11 ) = 1
x=-9
a.
x=6
b.
x=9
c.
x=-6
d.
80 Find the solution of the equation 4 -x = 64
a.
b.
c.
d.
x=-4
x=-3
x=4
x=7
88 Solve the system :
a.
no solution
b.
( 3, 11 )
c.
( 11, 3 )
d.
( 0, 0 )
89 The price of admission to a high school play was $3 for students and $6 for nonstudents. If 250 tickets were sold for a total of $981, how many of each kind were
purchased?
a.
b.
c.
d.
e.
91
62 non-students
173 students
77 non-students
188 students
178 students
Find the partial fraction decomposition.
a.
b.
c.
95
Find the third term of the sequence { 17 - 6 n } .
a3 = 17
a.
a3 = 23
b.
a3 = -7
c.
a3 = -1
d.
98
Find the sum
S = 35
a.
S = 39
b.
S = 37
c.
S = 22
d.
102 Find the sum of the arithmetic sequence Sn that satisfies the stated conditions.
a.
b.
c.
d.
s = -80
s = -88
s = -86
s = -90
103 Insert five arithmetic means between 9 and 33.
a.
13, 17, 21, 25, 29
b.
13, 21, 26, 31, 29
c.
13, 19, 26, 25, 29
d.
13, 19, 24, 25, 29
110 If a deposit of $400 is made on the first day of each month into an account that pays
9% interest per year compounded monthly, determine the amount in the account after
12 years.
a.
b.
c.
d.
$103857.76
$103861.81
$103867.81
$103084.63
111 After being discounted 30%, a radio sells for $67.90. Find the original price.
a.
$102.00
b.
$99.00
c.
$89.00
d.
$98.00
e.
$97.00
3 If a and h are real numbers, find f ( a ) + f ( h ) if f ( x ) = x2 - x + 2
a.
b.
c.
d.
f ( a ) + f ( h ) = a2 + h2 - a - h + 4
f ( a ) + f ( h ) = a2 + h2 + a + h
f ( a ) + f ( h ) = a2 + h2 + a + h + 4
f ( a ) + f ( h ) = a2 + h2 - a - h
4
If a is a positive real number, find
a.
b.
c.
6
Find the domain of f.
a.
b.
c.
d.
7 Find the domain of f.
a.
b.
c.
d.
if
10 Simplify the difference quotient
if
f ( x ) = x2 + 4
a.
b.
c.
d.
12 A hot-air balloon is released at 1:00 PM and rises vertically at a rate of 2 m/sec. An
observation point is situated a meters from a point on the ground directly below the
balloon (see the figure). If t denotes the time (in seconds) after 1:00 PM, express the
distance d between the balloon and the observation point as a function of t.
a = 125
a.
b.
c.
d.
16 The graph of a function f with domain [0, 4] is shown in the figure.
Sketch the graph of the equation
y = f (x + 3)
a.
b.
c.
21 Find the minimum value of the function f (x) = x2 + 6 x + 16
a.
b.
c.
d.
f (-3) = 7
f (7) = 3
f (2) = 6
f (0) = 16
22 A piece of wire 44 inches long is bent into the shape of a rectangle having width x and
length y. Express the area A of the rectangle as a function of x.
a.
b.
c.
A = -x2 + 22x
A = (x - 22) 2
A = x2 + 44x
23 Let f (x) = 5 x + 2, g (x) = x 2. Find:
a.
b.
c.
d.
e.
24 Let
Find the domain of: fg
a.
b.
c.
d.
e.
28 Solve the equation if f (x) = x 2 - 36, g (x) = x + 4.
a.
b.
c.
d.
e.
31 Find the inverse function of
a.
b.
c.
d.
34 Find all values of x such that f (x) < 0. f (x) = 36 x - x3
a.
b.
c.
37 If one zero of f (x) = x3 - 4 x2 - 25 x + 100 k is 4, find two other zeros.
a.
b.
c.