# College Algebra Fall Midterm Final Exam Name

```College Algebra
Fall Midterm Final Exam
Name
Part 1: Multiple Choice
(No Calculator – 2 points each)
Choose the one alternative that best completes the statement or answers the question.
1) Find and simply the difference quotient of f,
f ( x  h)  f ( x)
, h  0 , for the function f ( x )  x 2  3x  5 .
h
a) 1
2 x 2  2 x  2 xh  h 2  h  10
b)
h
c) 2 x  h  3
d) 2 x  h  5
2) Determine the domain of the function: f ( x)  3  2 x
3 
a)  ,  
2 
3

b)  , 
2

3 
c)  ,  
2 
3 3 

d)  ,   ,  
2 2 

3) Determine the domain of the function: h( x) 
a)  , 2
 2,  
b)  ,  
c)  , 8
d)  ,0
 8,0  0,8 8, 
 0, 
x2
x  64 x
3
4) Divide 21x 2  6 x 3  4  11x by 2x  5 .
a) 3x 2  3x  2 
6
2x  5
b) 3 x 2  3 x  2 
6
2x  5
c) 3 x 2  3 x  2 
14
2x  5
d) 3 x 2  3 x  2 
14
2x  5
5) Given the function g ( x) 
a)
n2  8
2n  4
b)
n 2  4n  2
2n  2
c)
n 2  4n  2
2n  4
d)
n2  6
2
2n
x2  6
, find g (n  2) . Simplify completely.
2x
 x  4, x  0
6) Determine the graph of the function f ( x)  
 4 x  1, x  0
a)
b)
c)
d)

7) Find the slope-intercept form of the equation of the line that passes through (2, 2) and is
perpendicular to the line x  4 y  24 .
1
5
a) f ( x)   x 
4
2
b) f ( x)  4 x  10
c) f ( x)  4 x  6
d) f ( x) 
1
x6
4
8) Solve x 2  5 x  6  0 for x.
a) x = -6, x = 1, x = -2, x = -3
b) x = -6, x = 1
c) x = 6, x = -1, x = 2, x = 3
d) x = 6, x = -1
9) Divide
 6  2i
and write the result in the standard form a  bi .
5  4i
a)
 22 14i

41
41
b)
 38 14i

41
41
c)
 22 34i

41
41
d)
 38 34i

41
41
10) What is the equation that yields the graph at right?
a) ( x  3) 2  ( y  4) 2  16
b) ( x  4) 2  ( y  3) 2  4
c) ( x  3) 2  ( y  4) 2  4
d) ( x  4) 2  ( y  4) 2  16
11) A model for the demand of wood saws is d  2 p 2  316 p  160 where d is the number of saws a
manufacturer can sell at a price of p dollars each. Find the price that will yield the maximum demand for
saws.
a) \$40
b) \$79
c) \$158
d) \$12,322
12) Perform the indicated operation and simplify the result. Leave the answer in factored form.
x 2  12 x  35
x2  9x

x 2  16 x  63 x 2  2 x  35
a)
x
x  16 x  63
b)
1
x7
c)
x ( x  9)
x7
d)
x
x7
2
13) Find the real solutions of the equation:
x2
3

.
x
x2
a) 4, 1
b) 2, 1
c) 4,1
d) 2,1
14) Perform the indicated operation and simplify the result. Leave the answer in factored form.
4
6
 2
x  3x  2 x  1
2
a)
48 x  8
( x  1)( x  1)( x  2)
b)
10 x  8
( x  1)( x  2)
c)
10 x  8
( x  1)( x  1)( x  2)
d)
8 x  10
( x  1)( x  1)( x  2)
15) Solve the inequality. Express your answer by graphing the solution set on a number line.
7x  6  4  0
a)
b)
c)
d)
16) Identify the equation for the function graphed at right.
a) f ( x ) 
1
( x  3) 2  4
2
b) f ( x )  2( x  3)2  4
1
c) f ( x )  ( x  3) 2  4
3
d) f ( x ) 
2
( x  3) 2  4
5
17) For the function f ( x )  2 x 2  3x , find the average rate of change from 1 to x.
a) 2
b) 2 x  1
2 x 2  3x  1
c)
x 1
d) x  1
College Algebra
Fall Midterm Final Exam
Name
Part 2: Problem Exercises
(Yes Calculator)
You must show ALL work and reasoning to receive full credit.
Solve the following equations in the complex number system (4 points each):
18) 12 x4  10x3  12 x2  0
19) 16 x3  12 x 2  4 x  3
20) x 2  x  3  0
21) Determine the standard form of the equation of a circle with endpoints of a diameter
at (6, -8) and (-4, -4). (6 points)
22) Determine the standard form of the equations of the circle with equation x 2  y 2  6 x  4 y  12  0
and graph the equation on the coordinate plane provided. (4 points)
1
1
23) For the polynomial f ( x )  0.02( x  1)( x  5) 2 ( x  3)3 :
a) Determine the degree of the polynomial. (1 point)
b) Determine the x- and y-intercepts of the graph. (3 points)
c) Graph f using a graphing utility.
d) Determine the local maxima and local minima, if they exist, rounded to two decimal places. (2 points)
e) Determine the intervals where f is increasing and where f is decreasing. (2 points)
f) Determine the domain and range of f . (2 points)
```