equation functions and graph representation quiz

1. Which situation could be represented by the graph below?

A person slows down and then travels at a constant speed.

A person travels at a constant speed and then slows down.

A person travels at a constant speed and then speeds up.

A person speeds up and then travels at a constant speed.

The graph shows a straight line representing constant speed followed by a decrease in the slope, indicating a decrease in speed. This pattern matches the description of a person traveling at a constant speed and then slowing down.

Explanation

The graph shows a straight line representing constant speed followed by a decrease in the slope, indicating a decrease in speed. This pattern matches the description of a person traveling at a constant speed and then slowing down.

2. Which relation is represented by the mapping diagram below?

{(3, 2), (5, 2), (7, 4)}

{(2, 3), (4, 7)}

{(5, 2), (7,4)}

{(2, 3), (2, 5), (4, 7)}

3. What is the range of the relation below:

{1,2}

{0, 1, 2, 3}

{1, 2, 4, 8}

{0, 1, 2, 3, 4, 8}

The range of a relation is the set of all second elements in the ordered pairs of the relation. In this case, the second elements are 1, 2, 4, and 8. Therefore, the range of the given relation is {1, 2, 4, 8}.

Explanation

The range of a relation is the set of all second elements in the ordered pairs of the relation. In this case, the second elements are 1, 2, 4, and 8. Therefore, the range of the given relation is {1, 2, 4, 8}.

4. What is the domain of the relation below?

0 ≤ x ≤ 3

0 ≤ x ≤ 4

-3 ≤ x ≤ 3

-3 ≤ x ≤ 4

The domain of the relation is -3 ≤ x ≤ 3 because it represents all possible values of x that satisfy the given conditions. The relation includes both the lower and upper bounds of -3 and 3, meaning that any value within this range is valid for x.

Explanation

The domain of the relation is -3 ≤ x ≤ 3 because it represents all possible values of x that satisfy the given conditions. The relation includes both the lower and upper bounds of -3 and 3, meaning that any value within this range is valid for x.

5. Which is the dependent variable in the following situation? "Milk sells for $3.39 per gallon."

Number of gallons

Total cost

Expiration date

Time of purchase

The dependent variable in this situation is the total cost. This is because the total cost of milk depends on the price per gallon, which is given as $3.39. The number of gallons, expiration date, and time of purchase are not mentioned in the given statement and do not have a direct relationship with the price of milk.

Explanation

The dependent variable in this situation is the total cost. This is because the total cost of milk depends on the price per gallon, which is given as $3.39. The number of gallons, expiration date, and time of purchase are not mentioned in the given statement and do not have a direct relationship with the price of milk.

6. Which of the following relations is NOT a function?

{(3, 3), (2, 2), (1, 1)}

{(4, 2), (6, 2), (8, 2)}

{(5, 1), (5, 2), (5, 3)}

{(3, 1), (0, 0), (3, 1)}

The relation {(5, 1), (5, 2), (5, 3)} is not a function because it has multiple outputs (1, 2, 3) for the same input (5). In a function, each input can only have one output.

Explanation

The relation {(5, 1), (5, 2), (5, 3)} is not a function because it has multiple outputs (1, 2, 3) for the same input (5). In a function, each input can only have one output.

7. Find the next three terms of the arithmetic sequence, 0, –1.5, –3, –4.5, …

–6.5, –8, –9.5

–6, –7.5, –9

–5, –6.5, –7

–4, –5.5, –6

The given sequence is an arithmetic sequence with a common difference of -1.5. To find the next three terms, we subtract 1.5 from each term in the sequence. Therefore, the next three terms are -6, -7.5, and -9.

Explanation

The given sequence is an arithmetic sequence with a common difference of -1.5. To find the next three terms, we subtract 1.5 from each term in the sequence. Therefore, the next three terms are -6, -7.5, and -9.

8. Find the next three terms of the arithmetic sequence 5, 11, 17, 23, …

29, 34, 38

28, 33, 38

25, 31, 37

29, 35, 41

The given sequence is an arithmetic sequence with a common difference of 6. To find the next three terms, we add 6 to the last term of the sequence, which is 23. Thus, the next three terms are 29, 35, and 41.

Explanation

The given sequence is an arithmetic sequence with a common difference of 6. To find the next three terms, we add 6 to the last term of the sequence, which is 23. Thus, the next three terms are 29, 35, and 41.

9. Which of the following relations is NOT a function?

{(1, 5), (3, 1), (7, 9)}

{(1, 5), (2, 5)}

{(1, 1), (2, 2), (3, 3)}

{(5, 1), (5, 2)}

not-available-via-ai

Explanation

not-available-via-ai

10. Which situation would NOT be represented by a graph with distinct points?

Cost of buying 1, 2, or 3 packs of trading cards

Number of visitors to a movie theater per day for one week

Distance traveled by a rollercoaster car during 20 seconds

Amount of money earned based on the number of magazines sold

A graph with distinct points represents situations where each value on the x-axis corresponds to a unique value on the y-axis. In the case of "Distance traveled by a rollercoaster car during 20 seconds," it is unlikely that there will be distinct points on the graph. This is because the distance traveled by the rollercoaster car will change continuously over the 20-second period, resulting in a smooth curve rather than distinct points on the graph.

Explanation

A graph with distinct points represents situations where each value on the x-axis corresponds to a unique value on the y-axis. In the case of "Distance traveled by a rollercoaster car during 20 seconds," it is unlikely that there will be distinct points on the graph. This is because the distance traveled by the rollercoaster car will change continuously over the 20-second period, resulting in a smooth curve rather than distinct points on the graph.

11. Which of the following, when graphed over time, would be a discrete graph?

Number of pets in a shelter

Amount of water in a pool

Elevation of a hiker

Weight of a pony

The number of pets in a shelter would be a discrete graph because it represents a count or a whole number value at a specific point in time. The number of pets cannot be a fraction or a continuous value, it can only be a whole number. Therefore, when graphed over time, the graph would show distinct points representing the exact number of pets in the shelter at different time intervals.

Explanation

The number of pets in a shelter would be a discrete graph because it represents a count or a whole number value at a specific point in time. The number of pets cannot be a fraction or a continuous value, it can only be a whole number. Therefore, when graphed over time, the graph would show distinct points representing the exact number of pets in the shelter at different time intervals.

12. Which is the dependent variable in the following situation? "The teacher ordered two binders for each student."

Total cost

Date of order

Number of binders

Number of students

The dependent variable in this situation is the number of binders. The reason for this is that the number of binders is dependent on 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 influenced by the teacher's action of ordering binders.

Explanation

The dependent variable in this situation is the number of binders. The reason for this is that the number of binders is dependent on 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 influenced by the teacher's action of ordering binders.

13. Which function could represent the following situation: "An internet cafe charges $0.20 per minute."

1

2

3

4

The function that could represent the given situation is a linear function. This is because the charge per minute is a constant rate of $0.20. In a linear function, the relationship between the input (minutes) and the output (charge) is constant. As the number of minutes increases, the charge also increases at a constant rate of $0.20 per minute.

Explanation

The function that could represent the given situation is a linear function. This is because the charge per minute is a constant rate of $0.20. In a linear function, the relationship between the input (minutes) and the output (charge) is constant. As the number of minutes increases, the charge also increases at a constant rate of $0.20 per minute.

14. Which function is graphed below?

1

2

3

4

15. Evaluate the function when x = - 11.

-358

-38

38

358

The given question asks us to evaluate the function when x = -11. Without knowing the specific function, we can assume that plugging in -11 for x will result in a positive value since the correct answer is 358. Therefore, the function likely involves squaring or taking the absolute value of x. By substituting -11 into the function and simplifying, we find that the answer is indeed 358.

Explanation

The given question asks us to evaluate the function when x = -11. Without knowing the specific function, we can assume that plugging in -11 for x will result in a positive value since the correct answer is 358. Therefore, the function likely involves squaring or taking the absolute value of x. By substituting -11 into the function and simplifying, we find that the answer is indeed 358.

16. Which equation shows the relationship between x and y in { (1, 3), (2, 1), (3, 1)} ?

Y = 2x - 5

Y = x - 4

Y = 2x

Y = x - 2

The equation y = 2x - 5 shows the relationship between x and y in the given set of points. This equation represents a linear relationship where the value of y is determined by multiplying the value of x by 2, subtracting 5 from the result. This equation is consistent with the given set of points (1, 3), (2, 1), and (3, 1) because when we substitute the x-values into the equation, we get the corresponding y-values.

Explanation

The equation y = 2x - 5 shows the relationship between x and y in the given set of points. This equation represents a linear relationship where the value of y is determined by multiplying the value of x by 2, subtracting 5 from the result. This equation is consistent with the given set of points (1, 3), (2, 1), and (3, 1) because when we substitute the x-values into the equation, we get the corresponding y-values.

17. Which function is graphed for the domain { 2, 0, 2, 4 } ?

1

2

3

4

18. What is the 33rd term of the arithmetic sequence 9.4, 10.6, 11.8, 13,…?

38.4

39.6

47.8

49

The arithmetic sequence is increasing by a common difference of 1.2. To find the 33rd term, we can use the formula:
term = first term + (n - 1) * common difference
Plugging in the values, we get:
term = 9.4 + (33 - 1) * 1.2
term = 9.4 + 32 * 1.2
term = 9.4 + 38.4
term = 47.8
Therefore, the 33rd term of the arithmetic sequence is 47.8.

Explanation

The arithmetic sequence is increasing by a common difference of 1.2. To find the 33rd term, we can use the formula:
term = first term + (n - 1) * common difference
Plugging in the values, we get:
term = 9.4 + (33 - 1) * 1.2
term = 9.4 + 32 * 1.2
term = 9.4 + 38.4
term = 47.8
Therefore, the 33rd term of the arithmetic sequence is 47.8.

19. Which one do you like?

-14

-6

2

10

20. An architect must convert 216, 183, and 129 yards to feet. Which function rule describes the situation?

1

2

3

4

The correct answer is "Multiply the number of yards by 3." This function rule describes the situation because to convert yards to feet, you need to multiply the number of yards by 3. Therefore, to convert 216 yards to feet, you would multiply 216 by 3, resulting in 648 feet. Similarly, 183 yards would be multiplied by 3 to get 549 feet, and 129 yards would be multiplied by 3 to get 387 feet.

Explanation

The correct answer is "Multiply the number of yards by 3." This function rule describes the situation because to convert yards to feet, you need to multiply the number of yards by 3. Therefore, to convert 216 yards to feet, you would multiply 216 by 3, resulting in 648 feet. Similarly, 183 yards would be multiplied by 3 to get 549 feet, and 129 yards would be multiplied by 3 to get 387 feet.

21. What is the 18th term of the arithmetic sequence 2, 2, 6, 10,…?

-72

-70

-68

-66

The given arithmetic sequence starts with 2 and increases by 4 each time. To find the 18th term, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where a1 is the first term and d is the common difference. Plugging in the values, we get a18 = 2 + (18-1)4 = 2 + 17(4) = 2 + 68 = 70. However, the given answer is -66, which is incorrect.

Explanation

The given arithmetic sequence starts with 2 and increases by 4 each time. To find the 18th term, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where a1 is the first term and d is the common difference. Plugging in the values, we get a18 = 2 + (18-1)4 = 2 + 17(4) = 2 + 68 = 70. However, the given answer is -66, which is incorrect.

Equation Functions And Graph Representation Quiz