Identify the domain and range. Graph/plot the Points that represent the relation. Identify if the relation is function or not

1.  {(3, 0)(2,1) (1,2). (0.5), (1,4),(2,3), (3,2)}



2. {(-2, 3),(-1,3), (-1,3), (0, 3), (1,3), (1.3)} 1



3. y=2x+1
         x={-1,-2, 0,1,2}





4. Solve for y=x²
{X = -3,-2,-1,0,1,2, 3} 

Let's break down each part of the problem one by one:

### 1. Relation: \{(3, 0), (2, 1), (1, 2), (0.5, 1), (1, 4), (2, 3), (3, 2)\}

- **Domain**: The set of all x-values.  
  Domain = \{3, 2, 1, 0.5\}  
  Notice that some x-values repeat.

- **Range**: The set of all y-values.  
  Range = \{0, 1, 2, 3, 4\}  
  Since all the y-values are different or repeat multiple times.

- **Graph**: If we plot the points, we get the following points:  
  (3, 0), (2, 1), (1, 2), (0.5, 1), (1, 4), (2, 3), (3, 2)

- **Is it a function?**  
  A relation is a function if every x-value maps to exactly one y-value.  
  In this relation, some x-values (1, 2, 3) map to more than one y-value.  
  Therefore, **this relation is not a function**.

### 2. Relation: \{(-2, 3), (-1, 3), (-1, 3), (0, 3), (1, 3), (1, 3)\}

- **Domain**:  
  Domain = \{-2, -1, 0, 1\}  
  The set of distinct x-values.

- **Range**:  
  Range = \{3\}  
  All y-values are 3.

- **Graph**: Points are:  
  (-2, 3), (-1, 3), (0, 3), (1, 3)

- **Is it a function?**  
  A relation is a function if each x-value has exactly one y-value.  
  Here, every distinct x-value has the same y-value (3).  
  Therefore, **this relation is a function**.

### 3. Relation: \( y = 2x + 1 \), \( x = \{-1, -2, 0, 1, 2\} \)

- **Domain**:  
  The given domain is \( x = \{-1, -2, 0, 1, 2\} \).

- **Range**:  
  We calculate the y-values for each x:
  - When \( x = -1 \), \( y = 2(-1) + 1 = -2 + 1 = -1 \)
  - When \( x = -2 \), \( y = 2(-2) + 1 = -4 + 1 = -3 \)
  - When \( x = 0 \), \( y = 2(0) + 1 = 1 \)
  - When \( x = 1 \), \( y = 2(1) + 1 = 3 \)
  - When \( x = 2 \), \( y = 2(2) + 1 = 5 \)

  Range = \{-3, -1, 1, 3, 5\}

- **Graph**: Points are:
  (-1, -1), (-2, -3), (0, 1), (1, 3), (2, 5)

- **Is it a function?**  
  Yes, because for every x-value there is exactly one y-value.  
  Therefore, **this relation is a function**.

### 4. Relation: \( y = x^2 \), \( x = \{-3, -2, -1, 0, 1, 2, 3\} \)

- **Domain**:  
  The given domain is \( x = \{-3, -2, -1, 0, 1, 2, 3\} \).

- **Range**:  
  We calculate the y-values for each x:
  - When \( x = -3 \), \( y = (-3)^2 = 9 \)
  - When \( x = -2 \), \( y = (-2)^2 = 4 \)
  - When \( x = -1 \), \( y = (-1)^2 = 1 \)
  - When \( x = 0 \), \( y = 0^2 = 0 \)
  - When \( x = 1 \), \( y = 1^2 = 1 \)
  - When \( x = 2 \), \( y = 2^2 = 4 \)
  - When \( x = 3 \), \( y = 3^2 = 9 \)

  Range = \{0, 1, 4, 9\}

- **Graph**: Points are:
  (-3, 9), (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4), (3, 9)

- **Is it a function?**  
  Yes, because for every x-value there is exactly one y-value.  
  Therefore, **this relation is a function**.

### Summary:
1. **Not a function**: Repeated x-values with different y-values.
2. **Function**: Each x-value has one y-value.
3. **Function**: Linear equation with distinct x-values.
4. **Function**: Quadratic equation with distinct x-values.

Would you like a more detailed explanation or graph for any of these parts? 

### Follow-up Questions:
1. How do we determine the domain and range of more complex functions?
2. What is the graphical representation of a function?
3. What makes a relation not a function?
4. How can we use the vertical line test to identify functions?
5. What are some examples of quadratic functions?

### Tip:
Always remember that a relation is a function if and only if each x-value corresponds to exactly one y-value. This can be visually checked using the vertical line test on a graph.

Identify the domain and range. Graph/plot the Points that represent the relation. Identify if the relation is a function or not.
1. {(3, 0)(2,1) (1,2). (0.5), (1,4),(2,3), (3,2)}
2. {(-2, 3),(-1,3), (-1,3), (0, 3), (1,3), (1.3)}
3. y=2x+1 x={-1,-2, 0,1,2}
4. Solve for y=x² {X = -3,-2,-1,0,1,2, 3}

Learn how to identify the domain and range of given relations and determine if they represent functions. This problem covers relations, functions, linear equations, and quadratic equations, suitable for students in Grades 8-10.

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