https://file.aiquickdraw.com/mathbot/file/1726623923930e7eorhf2.jpg

The graph you provided shows a function with vertical asymptotes at \( x = -4 \) and \( x = 2 \), which means the function is undefined at these points. Therefore, the domain of the function consists of all real numbers except \( x = -4 \) and \( x = 2 \).

Thus, the domain is:

\[
(-\infty, -4) \cup (-4, 2) \cup (2, \infty)
\]

This excludes the points where the function has vertical asymptotes.

Would you like further explanation or have any questions?

Here are some related questions to expand on this topic:
1. How do you determine the range of this function from the graph?
2. What are vertical asymptotes, and why do they exist in this graph?
3. How would the graph change if there were no asymptotes?
4. Can you express the equation of this graph based on the asymptotes?
5. What happens to the function as \( x \) approaches \( -4 \) and \( 2 \)?

**Tip:** The domain of a rational function is the set of all x-values except where the denominator equals zero (causing undefined points).

What is the domain of the function shown in the graph below?

Understand how to determine the domain of a rational function with vertical asymptotes at x = -4 and x = 2 from a graph. This problem is ideal for Grade 9 students exploring asymptotic behavior and domain restrictions.

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