At a school, is a student's ID number a function of their last name? Assume there are students with the same last name.

Yes, because every student has a last name and an ID number.

No, because a single last name (input) could correspond to multiple different ID numbers (outputs).

Yes, because each student has a unique ID number.

No, because some last names are longer than others.

Consider the relation $T = \{(\text{apple}, \text{red}), (\text{banana}, \text{yellow}), (\text{grape}, \text{red})\}$. Is this relation a function?

Yes, because each input (fruit) has exactly one output (color).

No, because the output 'red' is paired with two different inputs.

Understand Relations and Functions Practice — Grade 8 math

Lesson 1: Understand Relations and Functions — Practice Questions

1. The relation $S = \{(1, 5), (2, 6), (3, 7), (2, 8)\}$ is not a function. The input value that is paired with more than one output is ___.
2. At a school, is a student's ID number a function of their last name? Assume there are students with the same last name.
- A. Yes, because every student has a last name and an ID number.
- B. No, because a single last name (input) could correspond to multiple different ID numbers (outputs).
- C. Yes, because each student has a unique ID number.
- D. No, because some last names are longer than others.
3. A relation is defined by the set of ordered pairs $R = \{(-3, 9), (0, 0), (3, 9), (5, 25)\}$. The set of all output values, known as the range, is {___}.
4. Consider the relation $T = \{(\text{apple}, \text{red}), (\text{banana}, \text{yellow}), (\text{grape}, \text{red})\}$. Is this relation a function?
- A. Yes, because each input (fruit) has exactly one output (color).
- B. No, because the output 'red' is paired with two different inputs.
5. Which of the following sets of ordered pairs represents a function?
- A. {(2, 4), (3, 6), (2, 8)}
- B. {(1, 5), (4, 9), (1, 3)}
- C. {(0, 1), (5, 1), (9, 2)}
- D. {(-1, 0), (-1, 1), (-1, 2)}
6. A relation is described by a mapping diagram where the input `5` has arrows pointing to `10` and `k`. For this relation to be a function, the value of `k` must be ___.
7. A relation is shown in the table below. Which statement is true? Input (x): 4, 6, 4, 7 Output (y): 8, 1, 9, 5
- A. The relation is a function because every input has an output.
- B. The relation is a function because some outputs are different.
- C. The relation is not a function because the input `4` has two different outputs.
- D. The relation is not a function because the number of inputs and outputs is different.
8. A table contains the points `(1, 3)`, `(9, 5)`, and `(x, 7)`. If adding the point `(1, 8)` makes the relation NOT a function, the value of `x` cannot be ___.
9. Which statement correctly describes a property of all functions?
- A. Different inputs must have different outputs.
- B. A single input can correspond to more than one output.
- C. Different inputs can correspond to the same output.
- D. The set of inputs and outputs must be the same size.