MATH 105 College Algebra
Final Exam Review Problems
Dr. H. Edward Donley
Spring 2014
1. Solve 2

12

2 x
 x .
2. Find an equation for the line containing (2, –3) and perpendicular to x – 2 y = 1.
3. You have $5000 to invest, part at 2% simple annual interest and part at 4%. If you wish to earn $130 from the combined investments in one year, use algebra to find the amount that you should place in each investment.
4. Use transformations to sketch the graph of y
  x

2

1 .
5. Let f ( x )
 x

1 and g ( x )
 x
2
1

1
. Find f o g and g o f.
6. Algebraically solve
3 x x


2
5

2 .
7. Use transformations to sketch the graph of y

2

3
 x
.
8. Find log
9
1
27
without using a calculator
9. Express 2 ln 𝑥 − ln(𝑥 + 1) +
1
2 ln⁡(𝑥 − 1) as a single logarithm.

Answers to Final Exam Review Problems
1. 4
2. y = –2 x + 1
3. $3500 at 2% and $1500 at 4%
4. Graphs of y
 x , y
 x

2 , y
  x

2 , and y
  x

2

1 , each with successively shorter dashes.
1.5
1
0.5
0.5
1 1.5
2 2.5
3
-0.5
-1
5. (f o g)(x) = x
2 x
2

1
. (g o f)(x) =
1 x
.
6. {x | –2 < x < 9}
7.
Graphs of 3 x
, 3
– x
,
–
3
– x
, and 2
–
3
– x
, each with successively shorter dashes. Reflect the graph of 3 x
horizontally, reflect it vertically, and then shift up 2.
8
6
4
2
2 1 1 2
2
4
6
8. – 3/2
9. ln 𝑥
2
√𝑥−1 𝑥+1