https://file.aiquickdraw.com/mathbot/file/1726589949276gfkjg7m5.jpg

The image contains four functions labeled under section "2.14" that need to be analyzed. The functions are:

1. \( f(x) = x^4 \)
2. \( f(x) = |x| - 3 \)
3. \( f(x) = \sqrt{x^2 + 2} \)
4. \( f(x) = \frac{1}{x^2} \)

Would you like to explore any specific aspect of these functions (e.g., domain, range, continuity, derivatives), or would you like a general analysis of each?

Here are five questions that may help expand your understanding of these functions:

1. What is the domain of each function?
2. How do the graphs of these functions look?
3. What are the derivatives of each function?
4. What are the critical points and local extrema for each function?
5. How do these functions behave as \(x \to \infty\) and \(x \to -\infty\)?

Tip: For functions involving square roots or denominators, check for any restrictions in the domain to avoid undefined values.

Analyze the following functions: f(x) = x^4, f(x) = |x| - 3, f(x) = √(x^2 + 2), f(x) = 1/x^2.

Explore the function analysis for f(x) = x^4, f(x) = |x| - 3, f(x) = √(x^2 + 2), and f(x) = 1/x^2. This problem covers function behavior, domain, range, and key calculus concepts, suitable for Grades 11-12.

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