Challenging Algebra Quiz - Test Your Algebra Skills Today

1. Which relation is expressed by the mapping diagram below?

{(3,-1), (6,4), (8,4)}

{(-1,3), (6,4), (4,8)}

{(8,4), (6,4), (4,-1)}

{(4,3), (6,-1), (8,4)}

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.

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.

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

F(m) = m + 0.20

F(m) = m/20

F(m) = 0.20m

F(m) = 20m

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.

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.

3. What is the range of the relation given? x = 3,6,8,9 and y = 0,5,6,7

{3, 6, 8, 9}

{0, 5, 6, 7}

{0, 6, 8, 9}

{3, 6, 6, 9}

To determine the range of the relation given by the sets of x and y values, we need to identify the possible y values (outputs) associated with the xxx values (inputs).

Given: x=3,6,8,9 and y=0,5,6,7

Assuming this is a mapping of each x value to each y value in a one-to-one relation (each x maps to each y exactly once), the range is simply the set of y values given.

Thus, the range of the relation is: {0,5,6,7}

Explanation

To determine the range of the relation given by the sets of x and y values, we need to identify the possible y values (outputs) associated with the xxx values (inputs).

Given: x=3,6,8,9 and y=0,5,6,7

Assuming this is a mapping of each x value to each y value in a one-to-one relation (each x maps to each y exactly once), the range is simply the set of y values given.

Thus, the range of the relation is: {0,5,6,7}

4. 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 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.

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.

5. Which situation would be represented by a graph with points that are not connected?

The temperature of soup as it cools to room temperature

The height of a plant as it grows

The distance traveled on a bike

The number of shoppers who visited a store each day of the week

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.

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.

6. Which relation could this graph represent?

{(1, 3.5), (2.5, 2), (3, 2)}

{(1, 4.5), (3.5, 2), (3, 2)}

{(3.5, 1), (2, 2.5), (2, 3)}

{(4.5, 1), (2, 3.5), (2, 3)}

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)}.

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)}.

7. Which of the following is NOT a function?

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

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

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

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

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.

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.

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

Y = x - 4

Y = 2x - 5

Y = 2x

Y = x – 2

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.

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.

9. Which of the following relations is a function?

{(1,-6), (3,-5), (1,0)}

{(0,5), (5,-1), (5,9)}

{(6,1), (6,2), (6,3)}

{(0,8), (1,7), (2,6)}

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.

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.

10. Which is the dependent variable in the following situation? ¨Milke 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. 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.

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.

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

Y = │x - 1│

Y = x - 1

Y = │x│- 1

Y = 2x + 6

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.

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.

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

F(y) = y/3

F(y) = 3y

F(y) = 3/y

F(y) = y – 3

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.

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.

13. What is the 18^th term of the arithmetic sequence 2, -2, -6, -10, ….

-72

-70

-68

-66

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.

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.

14. What is the domain of the relation below? (assume that all inequalities in the answers are inclusive)

-3 < x < 3

-4 > x > 2

4 < x < -2

-4 < x < 2

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.

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.

15. 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 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.

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.