Function Worksheets - Free Printable

Problem Overview:

The task involves determining whether each set of ordered pairs represents a function. A function is defined as a relation where each input (x-value) corresponds to exactly one output (y-value). If any x-value appears more than once with different y-values, the relation is not a function.

We will solve both parts of the problem step by step:

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Part A: Ordered Pairs

#### 1) \((10, 9), (-2, -16), (-7, 7), (5, 8), (8, -16), (-11, 9)\)
- Check for repeated x-values:
- All x-values are unique: \(10, -2, -7, 5, 8, -11\).
- Since no x-value is repeated, this set represents a function.
- Answer: Yes

#### 2) \((-7, 4), (-8, 3), (-7, -7), (-20, 8), (5, 9), (3, 1), (2, 6)\)
- Check for repeated x-values:
- The x-value \(-7\) appears twice with different y-values: \((-7, 4)\) and \((-7, -7)\).
- Since an x-value is repeated with different y-values, this set does not represent a function.
- Answer: No

#### 3) \((-13, 4), (7, -15), (-13, 9), (6, -12), (-18, 0)\)
- Check for repeated x-values:
- The x-value \(-13\) appears twice with different y-values: \((-13, 4)\) and \((-13, 9)\).
- Since an x-value is repeated with different y-values, this set does not represent a function.
- Answer: No

#### 4) \((15, -3), (-6, 9), (-3, 0), (-1, 16)\)
- Check for repeated x-values:
- All x-values are unique: \(15, -6, -3, -1\).
- Since no x-value is repeated, this set represents a function.
- Answer: Yes

#### 5) \((-4, 3), (5, -9), (11, 4), (9, 6), (5, -3), (8, -9), (1, 4)\)
- Check for repeated x-values:
- The x-value \(5\) appears twice with different y-values: \((5, -9)\) and \((5, -3)\).
- Since an x-value is repeated with different y-values, this set does not represent a function.
- Answer: No

#### 6) \((12, -18), (15, 1), (12, 5), (0, 9), (-5, -17)\)
- Check for repeated x-values:
- The x-value \(12\) appears twice with different y-values: \((12, -18)\) and \((12, 5)\).
- Since an x-value is repeated with different y-values, this set does not represent a function.
- Answer: No

#### 7) \((6, 0), (-12, -16), (-6, 16), (20, -7)\)
- Check for repeated x-values:
- All x-values are unique: \(6, -12, -6, 20\).
- Since no x-value is repeated, this set represents a function.
- Answer: Yes

#### 8) \((-2, -4), (-8, 3), (-7, -4), (-2, -8), (11, 6), (5, -4)\)
- Check for repeated x-values:
- The x-value \(-2\) appears twice with different y-values: \((-2, -4)\) and \((-2, -8)\).
- Since an x-value is repeated with different y-values, this set does not represent a function.
- Answer: No

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Part B: Graphs

#### 1)
- Examine the graph:
- Each x-value on the graph corresponds to exactly one y-value.
- There are no vertical lines that intersect the graph at more than one point.
- This graph represents a function.
- Answer: Yes

#### 2)
- Examine the graph:
- Each x-value on the graph corresponds to exactly one y-value.
- There are no vertical lines that intersect the graph at more than one point.
- This graph represents a function.
- Answer: Yes

#### 3)
- Examine the graph:
- Each x-value on the graph corresponds to exactly one y-value.
- There are no vertical lines that intersect the graph at more than one point.
- This graph represents a function.
- Answer: Yes

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Final Answers:

#### Part A:
1. Yes
2. No
3. No
4. Yes
5. No
6. No
7. Yes
8. No

#### Part B:
1. Yes
2. Yes
3. Yes

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Boxed Final Answer:

\[
\boxed{
\text{Part A: } \text{Yes, No, No, Yes, No, No, Yes, No} \\
\text{Part B: } \text{Yes, Yes, Yes}
}
\]