Notes on Relations and Functions worksheet with definitions, examples, and exercises.

I will solve the problem in the image by analyzing each section and filling in the missing information. Let's break it down step by step.

First, look closely:

The image is a worksheet titled "Notes Relations & Functions" with several sections:
1. Functions - Defining relations vs functions, vertical line test, domain, range.
2. Tables - A table with x and y values to determine if it represents a function.
3. Graphs - A graph to determine if it's a function using the vertical line test.
4. Mapping - A mapping diagram to determine if it's a function.
5. Set - A set of ordered pairs to determine if it's a function.

I need to fill in the blanks for each section based on the definitions and rules of functions.

Next, find information:

I will analyze each section one by one.

#### Section 1: Functions
- Relations: A relation is any set of ordered pairs.
- Functions: A function is a special type of relation where each input (x-value) has exactly one output (y-value).
- Vertical Line Test: If a vertical line intersects the graph at more than one point, it is not a function.
- Domain: The set of all possible input values (x-values).
- Range: The set of all possible output values (y-values).

#### Section 2: Tables
The table has:
- x: 15, 9, 15, 25
- y: 8, 17, 17, 21

For a relation to be a function, each x-value must correspond to only one y-value. Here, x=15 appears twice with different y-values (8 and 17), so this is not a function.

#### Section 3: Graphs
The graph shows a parabola opening upwards. Using the vertical line test, any vertical line will intersect the graph at most once, so this is a function.

#### Section 4: Mapping
The mapping shows:
- Domain: 2, 6, 7, 8
- Range: 4, 5, 6, 8

Each element in the domain maps to exactly one element in the range, so this is a function.

#### Section 5: Set
The set of ordered pairs is:
{(−1, 2), (−4, −2), (3, −5), (−1, 0)}

Here, x=−1 appears twice with different y-values (2 and 0), so this is not a function.

Then, review the findings:

Now I will fill in the blanks based on my analysis.

Final Answer:

Here is the completed worksheet:

Functions
- Relations: Any set of ordered pairs.
- Functions: A relation where each input has exactly one output.
- Vertical Line Test: If a vertical line intersects the graph at more than one point, it is not a function.
- Domain: The set of all possible input values (x-values).
- Range: The set of all possible output values (y-values).

Tables
- Function: No (because x=15 maps to both 8 and 17)
- Domain: {9, 15, 25}
- Range: {8, 17, 21}

Graphs
- Function: Yes (passes the vertical line test)

Mapping
- Function: Yes (each domain element maps to exactly one range element)
- Domain: {2, 6, 7, 8}
- Range: {4, 5, 6, 8}

Set
- Function: No (because x=−1 maps to both 2 and 0)
- Domain: {−4, −1, 3}
- Range: {−5, −2, 0, 2}

This completes the worksheet by correctly identifying which relations are functions and determining their domains and ranges.