Name _________________________________________________________ Date _________
Tell whether x and y show direct variation, inverse variation, or neither. Explain your reasoning.
1.
4.
y  x2
2.
x
5
8
11
14
y
7
14
21
28
3
x  y
4
3. xy  0.3
5.
x
8
4
2
1
y
32
16
8
4
6. In Exercises A - C, the variables x and y vary inversely. Use the given values to write an equation
relating x and y. Then find y when x  3.
A. x  6, y   5
B. x  1, y  7
C. x  3, y  2
3
What is the vertical and horizontal asymptotes of the following functions? State the domain and
range.
7.
f  x 
5
4
x
8.
y 
3
2
x 1
The graph shows the function y 
9. h x 
2x  3
4x  2
1
 k . Determine whether the value of each
x  h
constant h and k is positive, negative, or zero.
A.
B.
C.
2 x  12
a
in the form of g  x 
 k. Describe the graph of g as a
x3
xh
a
transformation of the graph of f  x  .
x
10. Rewrite g  x 
11. You start a small beekeeping business. Your initial costs are $500 for equipment and bees. You
estimate it will cost $1.25 per pound to collect, clean, bottle, and label the honey. How many pounds
of honey must you produce before your average cost per pound is $1.79? Justify your answer.
98
Algebra 2
Assessment Book
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All rights reserved.
12.
To balance the board in the diagram, the distance (in feet) of each animal from the center of the board must vary
inversely with its weight (in pounds). What is the distance of each animal from the fulcrum? Justify your answer.
13. Brass is an alloy composed of 55% copper and 45% zinc by weight. You have 25 ounces of copper. How many
ounces of zinc do you need to make brass?
14.
The current y in a certain circuit varies inversely with the resistance x in the circuit. If the current is 8 amperes
when the resistance is 20 ohms, what will the current be when the resistance increases to 25 ohms?
Rewrite the following functions in the form g  x  
a transformation of the graph of f  x  
3x  7
x2
15.
g  x 
18.
Perform the indicated operations
19.
16.
a
 k . Graph the function. Describe the graph of g as
x  h
a
.
x
g  x 
4x  2
x3
17.
g  x 
4 x  10
x5
x2  2x  3 x2  4x  3

x2  2x  8 x2  6x  8
14
6

x  7 x  18 x  9
x2  2 x x2  6 x  5

x5
3x
x2  3
x5

2
x  6 x  16
x2
2
Solve the following
4
1
x 1


x5 x
x5
20.
Five table tennis balls fit tightly in a rectangular box as shown below.
a. Write an expression for the volume V of the rectangular box
in terms of the radius r. Then rewrite the formula to express
the radius in terms of the volume.
b. Find the percent of the box’s volume that is occupied by the
table tennis balls. Use 3.14 for  .
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Algebra 2
Assessment Book
99