Let's solve each part of the worksheet one by one:

1. Ordered Pairs and Functions

We need to determine if each set of ordered pairs is a function, and then identify its domain and range.

Problem 1:

• Ordered pairs: {(1, -2), (-2, 0), (-1, 2), (1, 3)}

• Function?
  No. The input $x = 1$ is repeated, but with different outputs (-2 and 3). This violates the rule of a function where each input must map to exactly one output.

• Domain:
  {-2, -1, 1} (The set of all distinct $x$-values)

• Range:
  {-2, 0, 2, 3} (The set of all distinct $y$-values)

Problem 2:

• Ordered pairs: {(1, 1), (2, 2), (3, 5), (4, 10), (5, 15)}

• Function?
  Yes. Each input (x-value) is unique and maps to exactly one output (y-value).

• Domain:
  {1, 2, 3, 4, 5}

• Range:
  {1, 2, 5, 10, 15}

Problem 3:

• Ordered pairs: $\left\{ \left( 17, \frac{15}{4} \right), \left( \frac{15}{4}, 17 \right), \left( 15, \frac{17}{4} \right), \left( \frac{17}{4}, 15 \right) \right\}$

• Function?
  Yes. Each input (x-value) is unique and maps to exactly one output (y-value).

• Domain:
  {17, 15/4, 15, 17/4}

• Range:
  {15/4, 17, 17/4, 15}

Problem 4:

• Ordered pairs: $\left\{ \left( -\frac{3}{5}, 2 \right), \left( -\frac{3}{5}, -\frac{3}{5} \right), \left( \frac{3}{2}, -5 \right), \left( 5, 2 \right) \right\}$

• Function?
  No. The input $x = -\frac{3}{5}$ repeats with two different outputs (2 and -3/5), violating the function rule.

• Domain:
  {-3/5, 3/2, 5}

• Range:
  {2, -3/5, -5}

2. Relations Expressed as Graphing

We need to analyze each graph, identify its domain and range, and determine if it represents a function.

Problem 5:

• The points are: $(-2, 2), (0, 0), (2, 0), (0, -2)$

• Relation:
  {(-2, 2), (0, 0), (2, 0), (0, -2)}

• Domain:
  {-2, 0, 2} (The set of distinct $x$-values)

• Range:
  {-2, 0, 2} (The set of distinct $y$-values)

• Function?
  No. The input $x = 0$ maps to two different outputs (0 and -2), so it is not a function.

Problem 6:

• The points are: $(-2, -1), (-1, 0), (0, 1), (1, 2)$

• Relation:
  {(-2, -1), (-1, 0), (0, 1), (1, 2)}

• Domain:
  {-2, -1, 0, 1}

• Range:
  {-1, 0, 1, 2}

• Function?
  Yes. Each input (x-value) maps to exactly one output (y-value).

Would you like any specific details explained further? Here are five related questions:

1. What is the formal definition of a function?
2. How do you determine the domain and range from a set of ordered pairs?
3. What are the conditions under which a relation is not a function?
4. Can a function have repeated values in the range? Why or why not?
5. How can a vertical line test be used to determine if a graph represents a function?

Tip: In mathematics, the domain is the set of all possible inputs (x-values), while the range is the set of all possible outputs (y-values). Always check for repeated x-values to verify if a relation is a function.