https://file.aiquickdraw.com/mathbot/file/1727320388865v7k3x0m8.jpg

The graph shows a linear function with a segment starting at the point \((-4, -6)\) and continuing through to a point beyond the visible part of the graph, suggesting it is increasing as \(x\) increases.

### **Domain:**
The domain of the function is the set of all possible \(x\)-values for which the function is defined. From the graph:
- The function begins at \(x = -4\) and extends indefinitely to the right, covering all \(x\)-values greater than or equal to \(-4\).

Thus, the domain is:
\[
\boxed{[-4, \infty)}
\]

### **Range:**
The range of the function is the set of all possible \(y\)-values that the function can take. From the graph:
- The function starts at \(y = -6\) and increases as \(x\) increases. Since the line continues upwards, the range covers all \(y\)-values greater than or equal to \(-6\).

Thus, the range is:
\[
\boxed{[-6, \infty)}
\]

Let me know if you want more details or have questions.

Here are 5 questions for further exploration:
1. How do you determine the slope of this line from the graph?
2. What is the equation of the line in slope-intercept form?
3. If the graph extended leftward, how would the domain and range change?
4. What are the effects of changing the slope of this line?
5. How would the graph look if it had a maximum or minimum \(y\)-value?

**Tip:** When determining the domain and range, always check the horizontal and vertical extents of the graph.

What are the domain and the range of the function shown in the graph?

Explore how to determine the domain and range of a linear function. This problem involves analyzing the graph of the function, starting from (-4, -6) and continuing upwards. Suitable for Grades 8-10.

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