Functions Unit Review Practice
Connections Academy 8th Grade
Please only use this to check your answers.
1. Find the next three terms in the sequence.
3, 12, 21, 30...
A. 40, 50, 60
B. 38, 46, 54
C. 39, 48, 57 ***
D. 36, 32, 39
2. Identify the sequence as arithmetic, geometric, or neither.
1.6, 0.8, 0.4, 0.2,...
A. arithmetic
B. geometric ***
C. neither
3. 5 • 3n
A. 15, 30, 45, 60
B. 5, 15, 45, 135
C. 0, 15, 45, 135
D. 15, 45, 135, 405 ***
4. Use the funciton rule f(x) = x • |-1|x. Find the output f(2)
A. 4
B. 3
C. -2
D. 2 ***
5. 3x + y = 2
A.
B.
C.
D. ***
6. Do the data in the table represent a linear function? If so write a rule for the function.
x|-2|-1| 0| 1| 2|
y|-7| 1| 8|17|25|
A. yes;y = 8x + 9
B. yes;y = 8x + 8
C. yes;y = 1/8x + 8
D. no ***
7. Use the slope and two points to write a linear function rule for the graph.
A. y= -2x - 6
B. y= 2x - 6 ***
C. y= 1/2x - 6
D. y= 1/2x + 6
8. Which of the following expressions represents a quadratic function?
A. y = 4x - 2
B. y = 3x^2 + 2x + 1 ***
C. y = 2x + 3
D. y = 5 - 2x
9. Identify the vertex of the parabola defined by the function f(x) = -2(x-3)^2 - 5
A. (3,-5) ***
B. (-3,5)
C. (2,-5)
D. (-2,5)
10. Solve the following system of equations by graphing:
2x + y = 5
x - y = 3
A. (2,1)
B. (-1,2)
C. (1,2)
D. (2,-1) ***
1. The next three terms in the sequence 3, 12, 21, 30... can be obtained by adding 9 to each term. Therefore, the next three terms are 39, 48, 57. The correct answer is C. 39, 48, 57.
2. The sequence 1.6, 0.8, 0.4, 0.2,... is a geometric sequence because each term is obtained by dividing the previous term by 2. The common ratio in this sequence is 1/2. The correct answer is B. geometric.
3. The expression 5 • 3n represents a geometric sequence with a common ratio of 3. Starting with n = 1, the terms of the sequence would be 15, 45, 135, 405. The correct answer is D. 15, 45, 135, 405.
4. Using the function rule f(x) = x • |-1|x, we substitute x = 2 into the function to find f(2) = 2 • |-1|2 = 2 • 2 = 4. The correct answer is A. 4.
5. The equation 3x + y = 2 represents a linear function in two variables, x and y. However, the options are missing the possible answers. Please provide the options.
6. The data in the table do not represent a linear function because when x increases by 1, y does not increase by a constant amount. The correct answer is D. no.
7. Without the slope and two points, it is not possible to write a linear function rule for the graph. Please provide the slope and two points or the options for the question.
1. To find the next three terms in the sequence 3, 12, 21, 30..., we can observe that the pattern is increasing by 9 each time. Therefore, the next three terms would be 39, 48, and 57. So the correct answer is C. 39, 48, 57.
2. To identify the sequence 1.6, 0.8, 0.4, 0.2,..., as arithmetic, geometric, or neither, we can observe that each term is half of the previous term. This indicates a geometric sequence where each term is multiplied by a common ratio of 1/2. So the correct answer is B. geometric.
3. The expression 5 • 3n represents a geometric sequence where each term is obtained by multiplying the previous term by a common ratio of 3. To find the next three terms, we can multiply 5 by 3 repeatedly. So the next three terms would be 15, 45, and 135. Therefore, the correct answer is D. 15, 45, 135.
4. Using the function rule f(x) = x • |-1|x, we can substitute x=2 to find the output f(2). Firstly, evaluate |-1| which is equal to 1. Then, multiply 2 by 1 to get the output as 2. Therefore, the correct answer is D. 2.
5. The equation 3x + y = 2 represents a linear function, as it is in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, we need more information to determine the values of x and y or to solve for y in terms of x. Therefore, the correct answer is D. ***.
6. To determine if the data in the table represents a linear function, we can check if the differences in the y-values are constant. Looking at the differences, we can see that they are not constant, so the data does not represent a linear function. Therefore, the correct answer is D. no.
7. To write a linear function rule using the slope and two points, we need to determine the slope from the given points and then use either of the two points to write the equation in the form y = mx + b. Since the slope is not given and the two points are not provided, it is not possible to answer this question without more information. Therefore, the correct answer cannot be determined.