A table shows the number of items sold ($n$) and the profit ($P$) in dollars. |n: 10, 20, 10, 30|, |P: 50, 100, 55, 150|. Does this table represent $P$ as a function of $n$?

Yes, because all the profit values are positive.

No, because the input $n=10$ is associated with two different profit values.

Yes, because as the number of items sold increases, the profit increases.

No, because the input values are not in increasing order.

Consider the table |Input (a): -1, 0, 2, 0|, |Output (b): 5, 7, 9, 8|. Why does this table fail to represent $b$ as a function of $a$?

Because the input value 0 corresponds to two different outputs.

Because the output values are not in order.

Because one of the inputs is a negative number.

Because two different inputs have different outputs.

Functions Practice — Grade 8 math

Lesson 1: Functions — Practice Questions

1. Which of the following tables defines $y$ as a function of $x$?
- A. |x: 2, 5, 2|, |y: 4, 10, 5|
- B. |x: 1, 2, 3|, |y: 7, 7, 7|
- C. |x: 3, 4, 3|, |y: 9, 12, 10|
- D. |x: 0, 1, 1|, |y: 0, 2, 3|
2. The table shows a relationship between an input, $p$, and an output, $q$. |p: 5, 10, 15, 10|, |q: 3, 6, 9, 7|. This table does not define $q$ as a function of $p$. What input value violates the definition of a function? ___
3. A table shows the number of items sold ($n$) and the profit ($P$) in dollars. |n: 10, 20, 10, 30|, |P: 50, 100, 55, 150|. Does this table represent $P$ as a function of $n$?
- A. Yes, because all the profit values are positive.
- B. No, because the input $n=10$ is associated with two different profit values.
- C. Yes, because as the number of items sold increases, the profit increases.
- D. No, because the input values are not in increasing order.
4. The table below defines the cost ($C$) as a function of the number of guests ($g$). |g: 1, 3, 4, 6|, |C: 12, 36, 48, 72|. What is the output value when the input value is 4? ___
5. Consider the table |Input (a): -1, 0, 2, 0|, |Output (b): 5, 7, 9, 8|. Why does this table fail to represent $b$ as a function of $a$?
- A. Because the input value 0 corresponds to two different outputs.
- B. Because the output values are not in order.
- C. Because one of the inputs is a negative number.
- D. Because two different inputs have different outputs.
6. What does the vertical line test determine?
- A. Whether a graph represents a function.
- B. The domain of a function.
- C. The range of a function.
- D. The intercepts of a graph.
7. A vertical line intersects a graph at the points $(4, 5)$ and $(4, -5)$. What can be concluded about the graph based on the vertical line test?
- A. It represents a function.
- B. It does not represent a function.
- C. It must be a circle.
- D. More information is needed.
8. The graph of the equation $x = y^2$ is not a function. A vertical line at $x=36$ intersects this graph at two points. The positive y-coordinate of one intersection point is ___.
9. Which of the following equations describes a graph that would fail the vertical line test?
- A. $y = x^2 + 5$
- B. $y = 2x - 1$
- C. $x^2 + y^2 = 16$
- D. $y = x$
10. The graph of the circle $x^2 + y^2 = 81$ is not a function. The vertical line $x=0$ intersects the graph at $(0, 9)$ and $(0, ext{\_\_\_})$.