https://file.aiquickdraw.com/mathbot/file/1726576510032atyfyx5d.jpg

The graph you've provided appears to be that of a cubic or quartic function. To determine the **domain** and **range** of the function, we can analyze the behavior of the graph.

### 1. Domain:
The domain of a function refers to all possible input values (x-values) for which the function is defined.

- From the graph, the function continues indefinitely both to the left and right along the x-axis. Hence, there are no restrictions on the x-values.
- The **domain** is:  
  \[
  \boxed{(-\infty, \infty)}
  \]

### 2. Range:
The range of a function refers to all possible output values (y-values) that the function can produce.

- From the graph, it seems that the curve descends infinitely in the negative y-direction (below -6) and ascends infinitely in the positive y-direction (above 4). 
- Hence, the **range** is also:  
  \[
  \boxed{(-\infty, \infty)}
  \]

Would you like more details or have any specific questions?

### Related questions:
1. How would the graph change if a constant was added to the function?
2. What are the critical points of this function (maxima, minima, or points of inflection)?
3. How can you determine the type of function (cubic, quartic, etc.) from the graph?
4. Can you find the intervals where the function is increasing or decreasing?
5. How do transformations like shifting or scaling affect the domain and range?

### Tip:
Remember that when analyzing a graph, always look for key points like intercepts, turning points, and asymptotic behavior to understand the function's characteristics.

Learn how to determine the domain and range of a cubic or quartic function by analyzing its graph. The function appears to extend infinitely in both the positive and negative directions for both x and y values. This tutorial is suitable for high school students, Grades 10-12.

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