To find the value of $f(x)$ when $x = 3$, we simply substitute $x = 3$ into the function $f(x) = 8 - 3x^2$:

$f(3) = 8 - 3(3)^2$

Now, calculate $3^2 = 9$:

$f(3) = 8 - 3(9) = 8 - 27 = -19$

So, the value of $f(3)$ is $-19$.

Would you like more details or have any questions about this?

Here are 5 related questions to expand your understanding:

1. What is the general process to evaluate any function $f(x)$ for a given $x$?
2. How would the function behave for negative values of $x$?
3. Can you find $f(x)$ when $x = -2$?
4. What does the graph of $f(x) = 8 - 3x^2$ look like?
5. How does the coefficient of $x^2$ affect the shape of a quadratic function?

Tip: When evaluating functions, always remember to apply the correct order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).