Let's go through each part systematically. For every part, we will:

1. List the Domain: The set of all first components (x-values).
2. List the Range: The set of all second components (y-values).
3. Check if it's a Function: If every x-value maps to exactly one y-value, the relation is a function. Otherwise, it is not.

(a) $\{(-4, -3), (2, -5), (4, 6), (2, 0)\}$

• Domain: $\{-4, 2, 4\}$
• Range: $\{-3, -5, 6, 0\}$
• Is it a Function?
  No, because $x = 2$ is mapped to both $-5$ and $0$.

(b) $\{(8, -2), (6, -\frac{3}{2}), (-1, 5)\}$

• Domain: $\{8, 6, -1\}$
• Range: $\{-2, -\frac{3}{2}, 5\}$
• Is it a Function?
  Yes, each x-value has a unique y-value.

(c) $\left\{(-\sqrt{3}, 3), (-1.1, 0), (0, 0), (1.1, 1.1), (\sqrt{3}, 3)\right\}$

• Domain: $\{-\sqrt{3}, -1.1, 0, 1.1, \sqrt{3}\}$
• Range: $\{3, 0, 1.1\}$
• Is it a Function?
  No, because both $x = -\sqrt{3}$ and $x = \sqrt{3}$ map to the same $y = 3$.

(d) $\left\{\left(-\frac{1}{2}, \frac{1}{6}\right), (-1, 1), \left(\frac{1}{3}, \frac{1}{3}\right)\right\}$

• Domain: $\left\{-\frac{1}{2}, -1, \frac{1}{3}\right\}$
• Range: $\left\{\frac{1}{6}, 1, \frac{1}{3}\right\}$
• Is it a Function?
  Yes, each x-value maps to a unique y-value.

(e) $\{(0, 5), (1, 5), (2, 5), (3, 5), (4, 5), (5, 5)\}$

• Domain: $\{0, 1, 2, 3, 4, 5\}$
• Range: $\{5\}$
• Is it a Function?
  Yes, each x-value has a unique y-value (even though all map to 5).

(f) $\{(5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)\}$

• Domain: $\{5\}$
• Range: $\{0, 1, 2, 3, 4, 5\}$
• Is it a Function?
  No, because $x = 5$ maps to multiple y-values (0, 1, 2, 3, 4, 5).

Summary

Do you have any further questions or want more details on specific parts?

5 Related Questions

1. What makes a relation not a function?
2. How is the domain different from the range?
3. Can a function have repeated y-values?
4. What is the difference between a function and a one-to-one function?
5. How do you determine the range when graphing a function?

Tip

Always check for repeated x-values with different y-values to quickly identify whether a relation is a function.