The function f(x) is defined as follows: $$ f(x) = \begin{cases} -4, & \text{if } -6 \le x < -2 \\ -x^2, & \text{if } -2 \le x < 0 \\ x^2, & \text{if } 0 \le x < 2 \\ 4, & \text{if } 2 < x < 8 \end{cases} $$

The function is defined piecewise. Let's break it down:

• For values of x between -6 (inclusive) and -2 (exclusive), the function f(x) equals -4.
• For values of x between -2 (inclusive) and 0 (exclusive), the function f(x) equals -x squared.
• For values of x between 0 (inclusive) and 2 (exclusive), the function f(x) equals x squared.
• For values of x between 2 (exclusive) and 8 (exclusive), the function f(x) equals 4.

This type of function is called a piecewise function because it has different rules for different intervals of x.