Functions
Name__________________________________
1. The monthly cost of operation at a company, C, given in dollars as a function of the number of units
produced per month, u, is given below.
C = 5,000 + 15u
Units Produced (u)
100
200
300
400
500
600
Monthly Cost (C)
?
?
?
?
?
?
Use the given equation to complete the table above.
A. 5,015; 5,030; 5,045; 5,060; 5,075; 5,090
B. 6,500; 6,515; 6,530; 6,545; 6,560; 6,575
C. 5,000; 6,500; 8,000; 9,500; 11,000; 12,500
D. 6,500; 8,000; 9,500; 11,000; 12,500; 14,000
2. Which expression represents the total volume of the pictures shown if each cube has a side length of e?
A. c3 + e3
B. c3 · e3
C. c3 · e
D. c · e3
3. Which of these mappings is a function?
W.
X.
Y.
Z.
A. W
B. X
C. Z
D. Y
5. The monthly cost of operation at a company, C, given in dollars as a function of the number of units
produced per month, u, is given below.
C = $3,173.00 + $31.00·u
If the company wants to keep the cost of operation under $16,000.00 per month, what's the maximum number
of units they can produce?
A. 4,130
B. 4,131
C. 413
D. 414
6. What is the range of the equation y = (x - 3)4 + 10?
A. {all real numbers less than or equal to -10}
B. {all real numbers greater than or equal to 10}
C. {all real numbers greater than or equal to -10}
D. {all real numbers less than or equal to 10}
7.
Using the vertical line test, determine if the graph above shows a relation, a function, both a relation and a
function, or neither a relation nor a function.
A. neither a relation nor a function
B. function only
C. both a relation and a function
D. relation only
8. Which of the following patterns is represented by the graph below?
A. 2n2 + n + 4
B. n2 + 5n - 3
C. n2 - 5n - 3
D. n2 - 4n - 3
9. Which of the following tables corresponds to the graph below?
A.
x
-3
-2
-1
0
y
3
8
7
/3
3
B.
x
-3
-2
-1
0
y
3
8
7
/3
3
C.
x
-3
-2
-1
0
y
3
8
7
D.
x
-3
3
y
/3
/3
/3
/3
2
-2
-1
0
8
7
/3
/3
2
1
5
/3
1
-5
/3
1
5
/3
1
-5
/3
10. The high school choir, the Warblers, are having a fundraiser. Tisha is the treasurer, and she created the
graph below to track how much money they are making the second week of the event. She plotted the
information at the end of each day with day one as the end of Monday.
Which equation in y-intercept form can she use to represent this graph?
Let x represent the number of days and y represent the amount of money in the account.
A. y = x + 100
B. y = 50x + 50
C. y = 50x + 1
D. y = x + 50
11.
What is the range of the function shown above?
A. {all real numbers less than or equal to 4}
B. {all real numbers}
C. {all real numbers greater than or equal to -2}
D. {all real numbers between -2 and 4}
12. Find the domain of the function below.
A. {all real numbers greater than negative two}
B. {all real numbers greater than or equal to negative two}
C. {all real numbers less than negative two}
D. {all real numbers}
13. Which of these mappings is a function?
W.
A. X
B. Z
C. Y
D. W
X.
Y.
Z.
14. Which of the following graphs is not a function?
A. X, Y, Z
B. Y and Z
C. Y
D. W, X, Y and Z
W.
X.
Y.
Z.
15. Which of these mappings is a function?
W.
X.
Y.
A. W
B. Y
C. X
D. Z
16. The first five terms of a sequence are given below.
41 , 43 , 45 , 47 , 49 , ...
Determine which of the following formulas gives the nth term of this sequence.
A. 43 - 2n
B. 42 - n
C. 40 + n
D. 39 + 2n
17. Which expression can be used to determine the nth term in the pattern below?
-6, -27, -62, -111, -174, ...
2
A. 7n - 1
B. -7n2 + 1
C. -7n + 1
D. -6n - 7
18. The elements of a function of x are (6, 7), (60, 16), and
(600, 106). What is the domain of the function?
A. {6, 7, 60}
B. {6, 60, 600}
C. {594}
D. {7, 16, 106}
Z.
19. Benny purchased a car for $15,900. The table below shows the amount of money that he still owes (y) after
each payment (x) that he makes.
Payment (x)
1
2
3
4
Amount Owed (y)
$15,625
$15,350
$15,075
$14,800
If Benny does not change his payment amount, how much money will he still owe after making his 6th
payment?
A. $13,975
B. $14,250
C. $14,525
D. $14,240
20.
(-6,1)
(-1,-4)
(1,-6)
(7,-12)
What is the range of the set of ordered pairs above?
A. {1, -12}
B. {-6, 1, 7, -12}
C. {1, -4, -6, -12}
D. {-6, -1, 1, 7}
Answers
1. D
2. B
3. C
4. C
5. C
6. B
7. D
8. C
9. C
10. B
11. B
12. D
13. B
14. C
15. A
16. D
17. B
18. B
19. B
20. C
x -3
y
3
-2
-1
0
8
7
2
/3
/3
1
5
/3
Explanations
1. Use the equation given to find the missing data in the table by substituting each value given for the variable u
into the equation and solving for C.
C = 5,000 + 15·(100) = 6,500
C = 5,000 + 15·(200) = 8,000
C = 5,000 + 15·(300) = 9,500
C = 5,000 + 15·(400) = 11,000
C = 5,000 + 15·(500) = 12,500
C = 5,000 + 15·(600) = 14,000
Therefore, to complete the table, the following values are needed: 6,500; 8,000; 9,500; 11,000; 12,500; 14,000.
2. The volume for each solid can be determined by multiplying the number of cubes by the volume of each
individual cube. Since the cubes each have a side length of e, the volume of each cube is e3.
Looking at the pattern, the number of cubes in each picture is always equal to c3.
Therefore, the total volume is given by c3 · e3.
3. A function maps each domain element to only one range element.
The only mapping that does not map a domain element to two or more range elements is Z.
4. The common difference in a linear pattern is equivalent to the slope of the correlating line.
In the graph above, the slope is 3.
Therefore, the common difference of the correlating pattern is also 3.
The only answer choice with a common difference of 3 is
3 , 6 , 9 , 12 , ....
5. Substitute $16,000.00 into the equation for C and solve the equation for u.
$16,000.00 - $3,173.00 = $31.00·u
$12,827.00 = $31.00·u
413.774... = u
Since the company wants their operating cost to be under $16,000.00 and a fraction of a unit can't be made, they
will only be able to make 413 units.
6. First, find the value of x that will make (x - 3) = 0, x = 3.
Knowing (x - 3) = 0 when x = 3, find y when x = 3. When x = 3,
y = 10, showing that either a minimum or a maximum occurs at (3, 10).
The degree of the function is even, meaning that the graph opens upward and that (3, 10) is a minimum.
Therefore, the range of the function is {all real numbers greater than or equal to 10}.
7. A relation is a set of one or more ordered pairs.
A function is a relation in which each element of the domain is paired with EXACTLY one element of the
range.
The Vertical Line Test: Given the graph of a relation, if a vertical line can be drawn that crosses the graph in
more than one place, then the relation is not a function.
The graph does not pass the vertical line test; therefore, the graph is not a function, and it is a relation only.
8. Substitute values of n into each pattern to find which gives the same coordinates as those on the graph.
The pattern n2 - 5n - 3 matches the graph as shown below.
n
0
1
2
3
4
5
6
n2 - 5n - 3
(0)2 - 5(0) - 3 = -3
(1)2 - 5(1) - 3 = -7
(2)2 - 5(2) - 3 = -9
(3)2 - 5(3) - 3 = -9
(4)2 - 5(4) - 3 = -7
(5)2 - 5(5) - 3 = -7
(6)2 - 5(6) - 3 = -7
(n, an)
(0,-3)
(1,-7)
(2,-9)
(3,-9)
(4,-7)
(5,-3)
(6, 3)
Therefore, the graph represents the pattern n2 - 5n - 3 because the pattern gives the same coordinates as those on
the graph.
9. The tables all have the same x-values: -3, -2, -1, 0, and 1.
The points on the graph with these x-values are shown below.
(-3,3), (-2,8/3), (-1,7/3), (0,2), (1,5/3)
Therefore, the following table corresponds to the graph.
x
y
-3
-2
-1
3
8
7
/3
/3
0
2
1
5
/3
10. To write an equation in y-intercept form, y = mx + b, the slope of the line, m, and the y-intercept, b, must be
known.
To determine b from a graph, identify the coordinate where the function crosses the y-axis. The y-value will be
b.
The coordinate is (0,50), so b = 50.
The slope can be found by picking two points of the graph and using the slope formula.
Let (x1,y1) = (0,50) and (x2,y2) = (1,100).
Use the slope formula with the coordinates above.
Putting it all together produces the equation for the line.
y = 50x + 50
11. The range of a function is the set of all output values, typically referred to as the y-values.
In the graph, the y-values are all real numbers.
Therefore, the range of the function is {all real numbers}.
12. In a function, the domain is the set of all real numbers that can be used for the independent variable, x.
The range is the set of all corresponding real numbers of the dependent variable, y.
Therefore, this function's domain is {all real numbers}.
13. A function maps each domain element to only one range element.
The only mapping that does not map a domain element to two or more range elements is Z.
14. A relation is a set of one or more ordered pairs.
A function is a relation in which each element of the domain is paired with EXACTLY one element of the
range.
The Vertical-Line Test: Given the graph of a relation, if a vertical line can be drawn that does not cross any of
the graphs in more than one place, it is a function.
Therefore, Y is not a function.
15. A function maps each domain element to only one range element.
The only mapping that does not map a domain element to two or more range elements is W.
16. A generic arithmetic sequence is of the following form,
a , a + d , a + 2d , a + 3d , ... , a + (n - 1)d , ...
where a is the first term, d is the common difference, and a + (n - 1)d is the nth term.
In this case, the first term is 41 and the common difference is 2.
Therefore, the nth term is as follows.
nth term = a + (n - 1)d
= 41 + (n - 1)(2)
= 41 + (2n - 2)
= 39 + 2n
17. The first and second differences of the sequence are shown below.
-6
-27
\
/
-21
-62
\
/
-35
-111
\
/
-49
-174
\
/
-63
\
/
\
-14
/
\
-14
/
-14
Since the second difference is constant, the pattern is quadratic with the form an2 + bn + c.
Set the second difference equal to 2a, and solve for a.
2a = -14
a = -7
Next, set the first term in the first difference equal to 3a + b, and solve for b.
3a + b = -21
3(-7) + b = -21
-21 + b = -21
b=0
Finally, set the first term in the pattern equal to a + b + c, and solve for c.
a + b + c = -6
-7 + 0 + c = -6
c=1
Therefore, the sequence can be represented by -7n2 + 1.
18. The domain of a function is the set of input values of a function.
In an ordered pair (x,y), it is represented by the x.
Therefore, the domain is {6, 60, 600}.
19. Use the table to determine the rate of decrease.
$15,625 - $15,350 = $275
$15,350 - $15,075 = $275
$15,075 - $14,800 = $275
The amount owed is decreasing at a rate of $275 per payment, and four payments have already been made. To
determine the amount owed after the 6th payment is made, subtract 2 more payments from the current amount
owed.
$14,800 - 2·$275 = $14,800 - $550 = $14,250
Therefore, the amount he will owe after the 6th payment is made will be $14,250.
20. The range of a set of ordered pairs is the set of y-coordinates.
In this set of ordered pairs, the y-coordinates are 1, -4, -6, and -12.
Therefore, the range is {1, -4, -6, -12}.