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Determine the value of f (–3) for the function  f of x is equal to the piecewise function x cubed plus 18 times x squared plus 104 times x plus 192 for x is less than negative 3 and the function quantity 3 times x plus 9 end quantity over the quantity x cubed plus 4 times x squared plus x minus 6 end quantity for negative 3 is less than or equal to x is less than 3 and the function square root of the quantity x squared minus 9 end quantity for x is greater than or equal to 3 period
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15

The value of \( f(-3) \) for the given piecewise function is \( 15 \).

Would you like more details or have any questions? Here are five related questions to expand on this topic:

1. How would you evaluate \( f(x) \) if \( x = 4 \)?
2. What happens to the function \( f(x) \) as \( x \) approaches 3 from the left?
3. How do you find the domain of the given piecewise function?
4. How would you find the derivative of the piecewise function?
5. What is the behavior of \( f(x) \) for large positive and large negative values of \( x \)?

**Tip:** When dealing with piecewise functions, always check which part of the function applies to the given value of \( x \) before evaluating.

Learn how to evaluate the piecewise function f(x) at x = -3. This problem involves understanding piecewise functions and evaluating different function rules based on given conditions. Suitable for high school students.

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