https://file.aiquickdraw.com/mathbot/file/1726541242445dwp6h0s6.jpg

From the graph, we are tasked with identifying various properties of the function \( f \). Let's start with part (a), which asks for the domain of \( f \) in interval notation.

### Domain of \( f \):
- The domain represents all the possible \( x \)-values for which the function is defined.
- In the graph, we can see that the parabola extends from \( x = -6 \) to \( x = 6 \) on the horizontal axis, without any breaks or gaps.
  
Thus, the domain of \( f \) is:
\[
\boxed{[-6, 6]}
\]

Would you like help with any of the other parts, or should we move on to the next one?

Here are 5 questions that expand upon the current understanding:
1. What is the range of \( f \) based on the graph?
2. How do you find the \( x \)-intercepts of a function?
3. What is the significance of the intervals on which \( f \) is increasing or decreasing?
4. How do you determine if a function is even, odd, or neither?
5. Can you explain how to find the relative minimum from the graph?

**Tip:** The domain of a function refers to the complete set of input values (typically \( x \)-values) for which the function is defined. Always check for gaps, holes, or restrictions in the graph to determine the domain.

Use the graph to find the following properties of the function f, such as domain, range, intercepts, intervals of increase or decrease, relative minimum, and symmetry.

Learn how to analyze the graph of a function to determine its domain, range, x-intercepts, y-intercept, increasing and decreasing intervals, relative minimum, and symmetry. This guide covers key concepts in graph analysis and function properties, suitable for high school students in Grades 9-12.

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