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The question asks for the creation of a graph of a function with the following key properties:

1. **Domain**: The function must have a domain of \((-\infty, \infty)\), meaning it is defined for all real numbers.
2. **Range**: The function must have a range of \((-\infty, \infty)\), meaning it takes all real values.
3. **Odd function**: The function must be odd, meaning it satisfies the condition \(f(-x) = -f(x)\). This implies symmetry about the origin.
4. **X-intercept**: The function must have one of its x-intercepts at the point \((-4, 0)\).

### Candidate Function
A simple function that satisfies these conditions is a cubic function. One possible cubic function that passes through \((-4, 0)\) is:
\[
f(x) = a(x + 4)(x)(x - b)
\]
Where:
- \(a\) is a constant that scales the function.
- \(b\) is another root of the function (because it should have another x-intercept).

Since this is an odd function, we can simplify it to a form that satisfies the conditions, such as:
\[
f(x) = a(x + 4)(x - 4)x
\]
This is a cubic function with odd symmetry, where \(f(-x) = -f(x)\), and one of its intercepts is at \((-4, 0)\).

Would you like a graph of this function or more details on how it satisfies each condition?

### Related Questions
1. What is the general form of an odd function?
2. How does changing the constant \(a\) affect the shape of a cubic function?
3. Why must an odd function be symmetric about the origin?
4. How would the function's graph change if we shifted the x-intercept from \((-4, 0)\) to another point?
5. What are other examples of functions that have both a domain and range of \((-\infty, \infty)\)?

**Tip**: Always ensure that odd functions have symmetry around the origin, which is essential for checking the function's oddness.

Create a beautiful graph of a function. Your function should have a domain of (-∞, ∞) and a range of (-∞, ∞). Make the graph an odd function with one of its x-intercepts located at (-4, 0).

Learn how to create a graph of an odd function with a domain of (-∞, ∞), range of (-∞, ∞), and one of its x-intercepts located at (-4, 0). This problem covers key concepts in algebra and graphing odd functions, suitable for Grades 10-12.

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