MAC 1105/Summer 2006
College Algebra
M. RAHMAN
Test 2 Review/sample questions
1. Solve the equations provided below. Be sure to check your answers.
x 2  5x  13  3
x  14  x  16
a)
b)
2. Solve the following equations:
9
 8
x2
x
7

 1
b) 2
x 9 x3
2
c) x  x  7 x  16
a) x 
3. Solve the inequality and write the solution using interval notation:
2x  5  7
a)
7  6x  3
b)
c) x  x  12  0
2
d) 2 x  5 x  12  0
4. Solve the following rational inequality:
2
5
1
x3
x 1
0
b)
x5
a)
5. Graph the following function:
a) f (x)  | x  3 | 2 ;
b) g ( x)  x  2, x  0 and
c) h(x) 
g ( x)  x 2  3, x  0 (piecewise defined function)
 ( x  3) 2  2
d) k ( x)  x  2  3
6. Find an equation of the line that passes through the point (3, -1) and is
perpendicular to the line 2 x  3 y  5 . Write the equation in slope-intercept form.
7. Solve the following system using substitution/elimination method method:
4 x  3 y  1
2x  5 y  3
8. Decide whether or not the following equation has a circle as its graph. If it does, give the center and the radius:
x 2  8 x  y 2  6 y  16  0
9. If g ( x)  5 x  2, calculate g (2), g ( 2  h), and
g ( x  h)  g ( x )
.
h
10. Evaluate ( f  g ) and ( g  f ) for the following functions
f (x)  x 2  5 ;
MAC 1147 Test 1 - M. RAHMAN
g ( x) 
Page 2
x2
11. Find domain and range of f , g , ( f  g ), and ( g  f ) for the following function
f (x)  3 x  5 ;
7
g ( x)  2
x 4
9. Find the vertex, domain, and range of the following quadratic functions
a) h(x) 
 ( x  3) 2  2
b) h( x)  5 x  10 x  3
Part II: Circle the Correct Choice
2
1. Given
f ( x)  2 x 2  6 x  5 , calculate f (1) .
(a) 12
(b) -3
(c) 9
(d) 1
(e) none of these
3x  1
, find g ( a  1) and simplify.
2 x
3a  2
3a  2
3a  2
(a)
(b)
(c)
3 a
3 a
3 a
2. Given g ( x ) 
3. Given the following graph of f ( x ) 
(d)
3a  2
2a
(e) none of these
( x 2  4) , determine the open interval(s)
in which the function is increasing or decreasing.
(a) increasing on (4, ), decreasing on (-, -2)
(b) increasing on (0, 4), decreasing on (0, 4)
(c) increasing on (2, ), decreasing on (-, 0)
(d) increasing on (0, ), decreasing on (-, -2)
(e) none of these
4. Determine whether the function f ( x )  3 x is even, odd, or neither.
(a) even (b) odd
(c) neither
(d) both even and odd
(e) none of these
f ( x )  x to obtain the
5. Describe the transformation that you apply to the graph of
graph of g ( x)   | x  2 | .
(a) shift 2 unit to the left, then reflect in the x axis
(b) shift 2 unit to the right, then reflect in the y axis
(c) shift 2 unit to the right, then reflect in the x axis
(d) shift 2 unit to the left, then reflect in the y axis
(e) none of these
6. The following graph of g(x) is the transformation of the graph of
an equation for g(x) .
f ( x )  x 2 . Find
(a)
g ( x )  ( x  3) 2  1
(b)
g ( x )  ( x  1) 2  3
(c)
g ( x )  ( x  3) 2  1
(d) g ( x )  ( x  1)
(e) none of these
S2006 Copyright 2006 University of North Florida
2
3