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Name_______________________Period_______Date_______Algebra 3 Test 4 -- 3.7, 4.1–4.3, 4.5
FUNCTIONS & RELATIONS
DEFINITIONS we’ll need:
a. Domain is known as ______________________________________________________________________.
b. Range is known as _______________________________________________________________________.
c. To determine if a graph is a function, we use the _______________________________________________.
I. Determine if the following relations are functions or not:
a.
d.
1,3 ,  0, 2  , 1, 4  , 3, 4 
5
3
b.
 5,3 ,  2,3 ,  6,3 ,  0,3
e.
-1
c.
 2,3 ,  2,3 , 5, 4 
f.
0
1
5
-3
0
6
2
-4
g.
h.
i.
j. y  7
k. 3 x  4 y  8
l. x  2
II. Find the domain and range of each function:
a.
 2,3 ,  2,1 ,  0,1 ,  4, 5 
b.
e. h( x) 
d. g ( x)  x  3
g.
 0, 6  ,  9, 6  , 1, 6  ,  2, 6 
h.
6
x 3
c. f ( x)  5 x  1
f. f ( x)  
i.
7
x8
SYSTEMS OF LINEAR EQUATIONS:
DEFINITIONS we’ll need:
a. Independent system:______________________________________________________________________.
b. Dependent system:_______________________________________________________________________.
c. Inconsistent system:______________________________________________________________________.
III. Determine if the following are solutions to the given system of linear equations:
2 y  4 x
a. 
1) (-3, -6)
2) (0, 0)
3) (1, 2)
2 x  y  0
2 x  y  1
b. 
3x  y  0
1) (3, -5)
2) (-1, 3)
3) (1, -3)
x  2 y  2
c. 
3x  2 y  2
1) (4, 1)
2) (-2, 2)
3) (0, -1)
IV. Solve the following systems by graphing. If a single point, write as an ordered pair:
y  x  2
a. 
 y  5 x  4
4 x  2 y  6
b. 
2 y  6  4 x
1
1
 2 x  4 y  1
c. 
y   2 x

3
 x  3 y  6
d. 
6 y  2 x  12
V. Solve the following systems by substitution. If a single point, write as an ordered pair:
6 x  7 y  9

a. 
1
 x  3 y  4
4 x  2 y  5
b. 
2 x  y  4
1
 x y 3
c.  2
 x  6  2 y
 y  2x  3
d. 
5 y  7 x  18
VI. Solve the following systems by elimination. If a single point, write as an ordered pair:
3x  y  5
3x  y  11
2 x  3 y  0
4 x  y  13
a. 
b. 
c. 
d. 
6 x  y  4
6 x  2 y  2
4 x  6 y  3
6 x  3 y  15
VII. Problem solving with systems:
a. The sum of two numbers is 62. The first number is six less than three times the second. What are the two
numbers?
b. The sum of two numbers is 17. The first number is two more than four times the second. What are the two
numbers?
c. The sum of two numbers is 84. The first number is nine less than twice the second. What are the two
numbers?
d. The sum of two numbers is 57. The first number is one more than three times the second. What are the two
numbers?
e. Bill needs to make 50 liters of a 42% alcohol solution. He currently has a 15% alcohol solution and a 60%
alcohol solution. How many liters of each does he need to make the 50 liters with a 42% alcohol solution?
f. A chemist needs to make 20 ounce solution that is 50% acid. She currently has a solution that is 20% acid
and a solution that is 60% acid. How many ounces of each does she need to make the 20 ounces of 50% acid
solution?
g. A manufacturer sells belts for $12 per unit. The manufacturer pays a $1600 operating fee plus $8 per unit.
How many belts must the manufacturer sell in order to break even?
h. A jewelry maker spends $1650 on operating costs and $35 for each necklace made. The necklaces are then
sold for $85 each. How many necklaces does the jewelry maker need to sell in order to break even?