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The problem displayed in the image asks you to find the natural domain and graph the function \( f(x) = 4 - 4x \).

### Solution:
1. **Natural Domain:**
   The function \( f(x) = 4 - 4x \) is a linear function. Linear functions are defined for all real numbers because there are no restrictions like division by zero or square roots of negative numbers. 
   
   **Domain:** The domain is \( \mathbb{R} \), which in interval notation is \( (-\infty, \infty) \).

2. **Graphing the Function:**
   The function \( f(x) = 4 - 4x \) can be rewritten as \( f(x) = -4x + 4 \), which is in the slope-intercept form \( y = mx + b \), where:
   - The slope \( m = -4 \)
   - The y-intercept \( b = 4 \)

   To graph the function:
   - Start at the point \( (0, 4) \) on the y-axis.
   - Use the slope \( -4 \) to find another point: go down 4 units and 1 unit to the right to reach the point \( (1, 0) \).
   - Draw a straight line through these points.

Would you like a detailed explanation of how to graph the function or have any other questions?

### Related Questions:
1. What are the steps to find the domain of a more complex function, like one involving square roots or fractions?
2. How does the slope of a linear function affect its graph?
3. Can you explain how to graph a function given in standard form instead of slope-intercept form?
4. What are the key characteristics of a linear function?
5. How can you find the range of a linear function?

### Tip:
When determining the domain of a function, always look out for restrictions like division by zero or taking square roots of negative numbers, as these often limit the domain to a subset of real numbers.

Find the natural domain and graph the function f(x) = 4 - 4x.

Explore the natural domain of the linear function f(x) = 4 - 4x and learn how to graph it. This problem involves core algebraic concepts, including the slope-intercept form and graphing linear functions. Ideal for students in Grades 9-11.

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