Name ________________________________
Algebra II-A
Unit 3 Test Review – Answers
1) a. V.A. x = 4 H.A. y = 0
b. V.A. x = -1 H.A. y = 4
2) Explain the end behavior of the graph of f  x  as it approaches its vertical asymptotes if
f  x 
3
x5
From the left, 𝑓(𝑥)∞
From the right, 𝑓(𝑥)−∞
3) Find the domain, x-intercepts, y-intercepts, horizontal asymptotes, and vertical asymptotes for
the following function. Show your work to verify your answers. Then, sketch a graph of the
function. Identify the coordinates of 6 points on your graph.
a. f  x  
1
4
x2
Domain: all reals except x  2
x - intercept = 
7
7
, y-intercept =
4
8
b. f  x   
1
2
x 1
Domain: all reals except x  1
x - intercept = 
3
, y-intercept = 3
2
4) Match each of the functions with its graph:
a. f  x  
1
2
x3
b. f  x  
1
3
x2
c. f  x  
1
2
x3
5) Write each of the functions in graphing form and then graph the function. Identify the vertical
and horizontal asymptotes and identify your key points.
a. f  x  
6x 1
6x 1
5
x 6
𝑦 =or f +
3x  1 𝑥 − 1
x 1
5 x  3−9
2x  3
b. f  x   𝑦 = or f+ 2
x 
𝑥+3
 x  10
x3
6)
Compare and contrast the graphs of f  x  
1
1
.
and f  x  
x
x
Reflection over the x-axis
7) Describe how to graph of h  x  
2
1
 5 as a transformation of the graph of f  x   .
x6
x
Shift left six units and down 5 units.
Stretch by a factor of 2.
8) You paid $120 for a membership to a racquetball club. Court time is $5 per hour. Write a model
that represents your average cost per hour of court time as a function of the number of hours
played. Graph the model. What is an equation of the horizontal asymptote and what does the
asymptote represent?
C  x 
120  5 x 120

5
x
x
Suppose that you can play racquetball at the YMCA for $9 per hour without being a member.
How many hours would you have to play at the racquetball club before your average cost per
hour of court time is less that $9? Solve algebraically and using a graph.
9) Find the least common denominator (LCD):
a.
1
12
, 2
x  6 x x  3x  18
b.
2
x  x  6 x  3
3x  1
3
, 2
2
x  7 x x  6x  7
c.
1
1
, 2
x  3x  28 x  6 x  8
x  x  7  x  1
2
 x  4 x  7 x  2
10) Perform the operations given:
a.
x
1
 2
x2 x 4
b.
x
1
 2
x2 x 4
 x  1
 x  2  x  2 
2
2x
x 1
e) 2

x  4 x  4 x( x  2)
c.
x2  2 x  1
 x  2  x  2 
3x
2
f)
 2
x  5 x  25
1
x 4
x
 x  2  x  2
x2  4
g)
2x  2
d.
2
2
3x 2  15 x  2
( x  5)( x  5)
(3x  2)( x  1)
x( x  2)2
x
x2
x2  5x  6
x2  6x  8
x
1
 2
x2 x 4
x  x  2
4x2
2x
h) 2

x  x6 x3
( x  2)( x  6)
2( x  4)
2x
x2
11) Solve:
a.
3
5

4x x  2
x
d.
6
17
3x
6
7


x  1 2x x
2
x   and 2
3
b.
x
x5

2x  7 x  1
x=-5 and 7
e.
10
4
5
 
x  2x x x  2
2
c.
3
6

x  2 x 1
x=-5
f.
x=2 (EXTRANEOUS, therefore, no solution)
2
x
2

 2
x 1 x 1 x 1
x=-4
x=1 Extraneous solution
12) An alloy is formed by mixing two or more metals. Sterling silver is an alloy composed of 92.5% silver
and 7.5% copper by weight. Jewelry silver is composed of 80% silver and 20% copper by weight. How
much pure silver should you mix with 15 ounces of jewelry silver to make sterling silver?
.925 
15(.8)  x
15  x
answer: 25 oz.
13) The coolant in a car radiator is a mixture of antifreeze and water. The recommended mixture for
your car is 50% antifreeze. If you have a mixture of 7 liters that is 40% antifreeze, how much antifreeze
should you add to bring the mixture up to the recommended level?
.5 
.4(7)  x
answer: 1.4 liters
7 x
14) Paint Mixing You have a 10 quart mixture of paint that is made up of equal amounts of red paint
and blue paint. To create a certain shade of purple, you need a paint mixture that is 75% blue. How
many quarts of blue paint do you need to add to the mixture?
Step 1: Verbal Model
Quarts of blue
paint in mixture
Quarts of paint
in mixture
+
+
Quarts of blue
paint needed
Quarts of blue
paint needed
Step 2: Write and solve equation
5+𝑥
10+𝑥
= .75
answer: 10 quarts
Step 3: Check solution
5+10
10+10
= .75
Solution works.
=
Desired percent
blue in mixture