Page 1
1.
For the function
1
() 2 +7
fx x
=
identify any A) vertical asymptotes and B) horizontal
asymptotes.
Enter the equation of the asymptote (use reduced fractions).
2.
For the function
3 – 5
() –5 – 3
x
fx x
=
identify any A) vertical asymptotes and B) any
horizontal asymptotes.
Enter the equation of the asymptote
( )
orx a y a==
, use reduced fractions.
3.
For the function
–5
() 4 +3
fx x
=
identify any vertical asymptotes.
Enter the equation of the asymptote (use reduced fractions).
4.
For the function
4 – 2
() –3 – 5
x
fx x
=
identify any vertical asymptotes.
Enter the equation of the asymptote
( )
xa=
, use reduced fractions.
5.
For the function
identify any horizontal asymptotes.
Enter the equation of the asymptote (use reduced fractions).
6.
For the function
7 – 8
() –8 – 3
x
fx x
=
identify any horizontal asymptotes.
Enter the equation of the asymptote
( )
xa=
, use reduced fractions.
7.
Identify any vertical asymptotes of the function
2
+3
() +3 +2
x
fx xx
=
.
Enter your answer as
xa=
,
xb=
, where
ab
.
8.
Start up costs for a small business are $100,000. Each product costs $2.50 to produce.
Construct a function for the total cost of producing x products.
Page 2
9.
Start up costs for a small business are $200,000. Each product costs $4.50 to produce.
Construct a function for the total cost per product.
10.
Evaluate the expression for x = 40. (Round the answer to two decimal places if
necessary.)
27
28
x
x
−
+
11.
Evaluate the expression for x = 25. (Round the answer to two decimal places if
necessary.)
2
2
2 5 1
4 3 3
xx
xx
+−
−+
12.
What values cannot be in the domain of this function?
39
() ( 5)(3 9)
x
fx xx
−
=−+
13.
State the domain of this function?
24
() ( 8)(2 8)
x
fx xx
−
=−+
14.
State the domain of this function?
2
8
() 2 14 20
x
fx xx
+
=++
15.
State the domain of this function?
2
b
() c d f
x
fx xx
+
=+−
16.
State the domain of this function?
2
5
() 3 12
x
fx x
+
=−
Page 3
17.
State the domain of this function?
1
() 3 15
x
fx x
+
=−
18.
Find the domain of the function
2
3
() 3 48
fx x
=−
19.
Find the domain of the function
2
4
() 59
fx x
=−
20.
Which equation describes the graph
A)
32
() 3
x
fx x
−
=−
B)
32
() 3
x
fx x
+
=+
C)
32
() 3
x
fx x
+
=−
D)
32
() 3
x
fx x
−
=+
Page 4
21.
Which equation describes the graph
A)
23
() 7
x
fx x
+
=−
B)
2
23
() 7
x
fx x
+
=+
C)
2
23
() 7
x
fx x
+
=−
D)
3
23
() 7
x
fx x
−
=−
22.
Decompose the rational function into a sum of a fraction and a constant.
4 31
() 8
x
fx x
−
=−
Page 5
Answer Key