MAC 1990/FALL2007
IntensiveCollege Algebra
EXAM2 Review/sample questions(SQ)
** To answer all questions in EXAM2, you must need to be the master of everything that I covered in sections 3.13.7, 4.1(light), 4.2(long division ONLY), 5.1-5.4.
Do all homework problems listed below, read class notes, and quizzes
§3.1 # 16, 20, 22, 24, 26, 28, 30, 32, 36, 38, 40, 42, 44, 46, 48, 50, 54
§3.2 # 24, 38, 40, 42, 56, 58, 78, 80
§3.4 # 2, 4, 6, 8, 10, 12, 14, 16, 18, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 70
§3.5 # 6, 8, 10, 12, 18, 22, 30, 40, 42
§3.6 # 2, 4, 6, 8, 10, 18, 20, 22, 24, 26, 28, 30,34, 38, 40, 50
§3.7 # 8, 10, 12, 18, 24, 30, 34, 36, 38, 40, 44
§4.2 # 6, 10, 14(Long Division)
§5.1 # 2, 14, 16, 18, 20, 22, 30, 32
§5.2 # 2, 4, 6, 8, 10, 12, 16, 22, 24, 26, 28, 30, 50, 54, 60
§5.3 # 1, 4, 6, 8, 14, 16, 18, 22, 24, 26, 32, 40, 42, 44, 50, 52
§5.4 # 2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 28, 0, 32, 34, 36, 8, 40, 42, 44, 46, 48, 50, 68, 74
SQ1. Find the domain of the following functions:
i) f ( x)  7  3x
ii) g ( x) 
x
2x  x  1
2
2 x  3, x  1
iii) f ( x)  
. Sketch the graph of f (x ) .
3  x, x  1
SQ2. If g ( x)  5 x  2, calculate g (2), g ( 2  h), and
g ( x  h)  g ( x )
.
h
SQ3. Evaluate ( f  g )(2) and ( g  f )(-1) for the following functions
f (x)  x 2  5 ;
g ( x) 
x2
SQ4. Find domain and range of f , g , ( f  g ), and ( g  f ) for the following function
f (x)  x  5 ;
7
g ( x)  2
x 4
MAC 1990 EXAM1 Review - M. RAHMAN
Page 2
SQ5. For the function f ( x)  2 x  4 , check whether the function is one-to-one or not. If one-to-one write an
equation for the inverse. Give the domain and range of f(x) and
f
1
f
1
( x) . Verify that f ( f
1
( x))  x and
( f ( x))  x .
SQ6. Find the vertex, domain, and range of the following quadratic functions
a) h(x) 
b)
 ( x  3) 2  2
h( x)  5x 2  10 x  3
SQ7. Find the quotient and remainder using long division.
3x 4  5 x 3  20 x  5
x3  x  3
x
SQ8. a. Graph the function f ( x)  2  1 .
b.
Find domain, range, and horizontal asymptote.
c.
Solve for x: 2
d.
Solve for x:
4
3 y
x2
8
 2 3 x 3
SQ9. a. Graph the function f ( x)  log 2 x .
b. Find domain, range, and vertical asymptote.
c. Write the following expression as a sum and/or difference of logarithms. Express power as factor:
x3 x  1
( x  2) 2
d. Solve for x: -2 log 4 x  log 4 9
e. Solve for x: log 4 ( x  6)  log 4 ( x  2)  log 4 x
log
F2007 Copyright 2007 University of North Florida