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What are the domain and the range of the function?


The given graph shows a linear function with specific endpoints. Let's analyze both the domain and the range of the function.

### 1. Domain:
The domain represents the set of all possible **x-values** for which the function is defined. 

From the graph:
- The function starts at \( x = -10 \) (on the left side) and continues up to \( x = 4 \) (on the right side).
- The endpoint at \( x = 4 \) is **open**, which means the function does not include this value, while the function includes the point at \( x = -10 \) (closed endpoint).

So, the domain is:
\[ \text{Domain} = [-10, 4) \]

### 2. Range:
The range represents the set of all possible **y-values** the function takes.

From the graph:
- At \( x = -10 \), the function starts with \( y = 0 \) and increases to \( y = 4 \) at \( x = 4 \) (but \( y = 4 \) is not included because of the open circle at the endpoint).
  
Thus, the range is:
\[ \text{Range} = [0, 4) \]

### Final Answer:
- Domain: \( [-10, 4) \)
- Range: \( [0, 4) \)

Would you like further details, or have any other questions?

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Here are 5 related questions:
1. How can you find the slope of this line from the graph?
2. What is the equation of the linear function shown in the graph?
3. How does an open or closed endpoint affect the domain or range of a function?
4. Can a function's domain be limited even though it is a linear function?
5. How would the range change if the open circle at \( x = 4 \) were filled in?

**Tip:** When determining the range, always focus on how the **y-values** change across the domain of the function!

What are the domain and the range of the function?

Understand how to find the domain and range of a linear function from its graph. This example analyzes the function's behavior between x = -10 and x = 4, focusing on how open and closed endpoints affect the solution. Suitable for students in Grades 6-8.

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