The set of ordered pairs `{(0, 0), (2, 4), (3, 6), (2, 5)}` does not represent a function. Which statement best explains why?

The input 2 is paired with two different outputs.

The output values are not always increasing.

Two different inputs have the same output.

Which of the following sets of ordered pairs $(x, y)$ represents a function?

A = {(-1, 1), (0, 2), (1, 3), (0, 4)}

B = {(5, 10), (6, 10), (7, 10), (8, 10)}

C = {(4, 2), (4, -2), (9, 3), (9, -3)}

D = {(1, 1), (1, 2), (1, 3), (1, 4)}

In a school, each student is assigned exactly one student ID number. If the student is the input and the ID number is the output, does this relationship represent a function?

No, because two different students must have two different ID numbers.

Yes, because each student has one and only one ID number.

No, because you cannot use a student as an input.

Yes, but only if the ID numbers are assigned in alphabetical order.

Functions Practice — Grade 8 math

Lesson 41: Functions — Practice Questions

1. The set of ordered pairs `{(0, 0), (2, 4), (3, 6), (2, 5)}` does not represent a function. Which statement best explains why?
- A. The output 0 is used.
- B. The input 2 is paired with two different outputs.
- C. The output values are not always increasing.
- D. Two different inputs have the same output.
2. The cost ($C$) to buy a number of notebooks ($n$) is given by the function $C = 4n$. How much will it cost to buy 6 notebooks? The cost will be ___ dollars.
3. Which of the following sets of ordered pairs $(x, y)$ represents a function?
- A. A = {(-1, 1), (0, 2), (1, 3), (0, 4)}
- B. B = {(5, 10), (6, 10), (7, 10), (8, 10)}
- C. C = {(4, 2), (4, -2), (9, 3), (9, -3)}
- D. D = {(1, 1), (1, 2), (1, 3), (1, 4)}
4. A function's rule states that the output $y$ is one less than twice the input $x$. The equation for this function is $y = $ ___.
5. In a school, each student is assigned exactly one student ID number. If the student is the input and the ID number is the output, does this relationship represent a function?
- A. No, because two different students must have two different ID numbers.
- B. Yes, because each student has one and only one ID number.
- C. No, because you cannot use a student as an input.
- D. Yes, but only if the ID numbers are assigned in alphabetical order.
6. Why is the equation $y = x + 8$ not a proportional relationship?
- A. It is not a linear equation.
- B. Its graph does not pass through the origin (0, 0).
- C. The output is always greater than the input.
- D. The equation does not contain multiplication.
7. The table below shows a proportional relationship between the number of cars ($x$) and the total number of wheels ($y$). What is the constant of proportionality, $k$? | Cars (x) | Wheels (y) | |---|---| | 1 | 4 | | 3 | 12 | | 5 | 20 | The constant of proportionality is ___.
8. Which of the following equations represents a proportional relationship between $x$ and $y$?
- A. $y = x - 3$
- B. $y = 7x$
- C. $y = 3x + 2$
- D. $y = x^2$
9. The cost to download songs is proportional to the number of songs purchased. If 3 songs cost 6 dollars, what is the cost in dollars for 8 songs? ___
10. Which of these tables shows a proportional relationship between $x$ and $y$?
- A. Table A: x=2, y=6; x=3, y=9; x=5, y=15
- B. Table B: x=1, y=5; x=2, y=6; x=3, y=7
- C. Table C: x=1, y=1; x=2, y=4; x=3, y=9
- D. Table D: x=0, y=4; x=1, y=5; x=2, y=6