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When it comes to graphs one has to know which the dependent is and independent variable and the different graphs that exist. Do you want to test out your algebra skills when it comes to graphs and interpreting them? Take up the quiz below and test yourself out. All the best!
Questions and Answers
1.
Which situation would be represented by a graph with points that are not connected?
A.
The temperature of soup as it cools to room temperature
B.
The height of a plant as it grows
C.
The distance traveled on a bike
D.
The number of shoppers who visited a store each day of the week
Correct Answer D. The number of shoppers who visited a store each day of the week
Explanation A graph with points that are not connected would represent the number of shoppers who visited a store each day of the week. In this situation, each point on the graph would represent the number of shoppers on a specific day, and since the points are not connected, it indicates that there is no relationship or pattern between the number of shoppers on different days.
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2.
Which relation is expressed by the mapping diagram below?
A.
{(3,-1), (6,4), (8,4)}
B.
{(-1,3), (6,4), (4,8)}
C.
{(8,4), (6,4), (4,-1)}
D.
{(4,3), (6,-1), (8,4)}
Correct Answer A. {(3,-1), (6,4), (8,4)}
Explanation The mapping diagram shows a relation where the first element of each ordered pair corresponds to the second element in a one-to-one manner. The answer choice {(3,-1), (6,4), (8,4)} is the only one that matches this pattern, as the first element of each ordered pair corresponds to the second element.
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3.
What is the domain of the relation below? (assume that all inequalities in the answers are inclusive)
A.
-3 < x < 3
B.
-4 > x > 2
C.
4 < x < -2
D.
-4 < x < 2
Correct Answer D. -4 < x < 2
Explanation The correct answer is -4 < x < 2 because it is the only option that satisfies the given inequalities. The other options either do not include the values of x that satisfy the inequalities or include values that do not satisfy the inequalities.
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4.
What is the range of the relation below?
x
3
6
8
9
y
0
5
6
7
A.
{3, 6, 8, 9}
B.
{0, 5, 6, 7}
C.
{0, 6, 8, 9}
D.
{3, 6, 6, 9}
Correct Answer B. {0, 5, 6, 7}
Explanation The range of a relation is the set of all second elements (y-values) in the ordered pairs of the relation. In this case, the second elements are {0, 5, 6, 7}, so the range of the relation is {0, 5, 6, 7}.
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5.
Which of the following relations is a function?
A.
{(1,-6), (3,-5), (1,0)}
B.
{(0,5), (5,-1), (5,9)}
C.
{(6,1), (6,2), (6,3)}
D.
{(0,8), (1,7), (2,6)}
Correct Answer D. {(0,8), (1,7), (2,6)}
Explanation The given relation {(0,8), (1,7), (2,6)} is a function because each input value (x-coordinate) is associated with only one output value (y-coordinate). In other words, there are no repeated x-values in the relation. This satisfies the definition of a function, where each input has a unique output.
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6.
Which equation shows the relationship between x and y in {(1, -3), (2, -1), (3, 1)}?
A.
Y = x - 4
B.
Y = 2x - 5
C.
Y = 2x
D.
Y = x – 2
Correct Answer B. Y = 2x - 5
Explanation The equation y = 2x - 5 shows the relationship between x and y in the given set of points. By substituting the x-values from the given points into the equation, we can see that the equation holds true for all the points. Therefore, y = 2x - 5 is the correct equation to represent the relationship between x and y in the given set of points.
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7.
Which function could represent the following situation: “An internet café charges $0.20 per minute.”
A.
F(m) = m + 0.20
B.
F(m) = m/20
C.
F(m) = 0.20m
D.
F(m) = 20m
Correct Answer C. F(m) = 0.20m
Explanation The function f(m) = 0.20m represents the given situation accurately. In this function, 'm' represents the number of minutes and 0.20 represents the charge per minute. By multiplying the number of minutes by 0.20, we can calculate the total charge for the internet café.
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8.
An architect must convert 216, 183, and 129 yards to feet. Which function rule describes the situation?
A.
F(y) = y/3
B.
F(y) = 3y
C.
F(y) = 3/y
D.
F(y) = y – 3
Correct Answer A. F(y) = y/3
Explanation The function rule f(y) = y/3 describes the situation because it converts yards to feet. Since there are 3 feet in 1 yard, dividing the number of yards by 3 will give the equivalent number of feet.
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9.
Evaluate the function when x = -6.
A.
-14
B.
-6
C.
2
D.
10
Correct Answer D. 10
10.
Which is the dependent variable in the following situation? “The teacher ordered two binders for each student.”
A.
Total cost
B.
Date of order
C.
Number of binders
D.
Number of students
Correct Answer C. Number of binders
Explanation The dependent variable in this situation is the number of binders. The reason is that the number of binders is directly influenced by the action of the teacher ordering them for each student. The other options, such as total cost, date of order, and number of students, are not directly dependent on the teacher's action of ordering binders.
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11.
Find the next three terms of the arithmetic sequence: 0, -1.5, -3, -4.5, …
A.
-6.5, -8, -9.5
B.
-6, -7.5, -9
C.
-5, -6.5, -7
D.
-4, -5.5, -6
Correct Answer B. -6, -7.5, -9
Explanation The given arithmetic sequence has a common difference of -1.5. To find the next three terms, we subtract -1.5 from the last term -4.5 to get -6, then subtract -1.5 from -6 to get -7.5, and finally subtract -1.5 from -7.5 to get -9. Therefore, the next three terms of the arithmetic sequence are -6, -7.5, and -9.
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12.
What is the 18^{th} term of the arithmetic sequence 2, -2, -6, -10, ….
A.
-72
B.
-70
C.
-68
D.
-66
Correct Answer D. -66
Explanation The arithmetic sequence starts with 2 and each term is obtained by subtracting 4 from the previous term. To find the 18th term, we can use the formula:
term = first term + (n-1) * common difference.
Plugging in the values, we get:
term = 2 + (18-1) * (-4) = 2 + 17 * (-4) = 2 - 68 = -66.
Therefore, the 18th term of the sequence is -66.
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13.
Which function is graphed for the domain {-2, 0, 2, 4}?
A.
Y = x - 1
B.
Y = │x│- 1
C.
Y = 2x + 6
D.
Y = │x - 1│
Correct Answer B. Y = │x│- 1
Explanation The correct answer is y = │x│- 1. This function is graphed for the given domain {-2, 0, 2, 4}. It represents the absolute value of x minus 1, which means that for any positive value of x, the function will be x - 1, and for any negative value of x, the function will be -x - 1. Since the domain includes both positive and negative values, this function is the most appropriate choice.
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14.
Which is the dependent variable in the following situation?
¨Milke sells for $3.39 per gallon.¨
A.
Number of gallons
B.
Total cost
C.
Expiration date
D.
Time of purchase
Correct Answer B. Total cost
Explanation The dependent variable in this situation is the total cost. The total cost depends on the number of gallons of milk sold, as each gallon is sold for $3.39. The other options, such as expiration date and time of purchase, do not directly affect the total cost of the milk.
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15.
Which of the following is NOT a function?
A.
{(1, 5), (3, -1), (7, 9)}
B.
{(1, 5), (2, 5)}
C.
{(1, 1), (2, 2) (3, 3)}
D.
{(5, 1), (5, 2)}
Correct Answer D. {(5, 1), (5, 2)}
Explanation The given set, {(5, 1), (5, 2)}, is not a function because it violates the definition of a function. In a function, each input (x-value) should have only one corresponding output (y-value). However, in this set, the input 5 has two different outputs, 1 and 2. Therefore, it does not satisfy the requirement of being a function.
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16.
Which relation could this graph represent?
A.
{(1, 3.5), (2.5, 2), (3, 2)}
B.
{(1, 4.5), (3.5, 2), (3, 2)}
C.
{(3.5, 1), (2, 2.5), (2, 3)}
D.
{(4.5, 1), (2, 3.5), (2, 3)}
Correct Answer A. {(1, 3.5), (2.5, 2), (3, 2)}
Explanation The given graph represents a relation where the x-values are increasing from left to right and the y-values are decreasing from top to bottom. The points on the graph show a trend where as the x-values increase, the y-values decrease. This can be observed by looking at the points (1, 3.5), (2.5, 2), and (3, 2). Therefore, the correct answer is {(1, 3.5), (2.5, 2), (3, 2)}.
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17.
Evaluate the function when x = -11.
A.
-358
B.
-38
C.
38
D.
358
Correct Answer D. 358
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