1. Let's clarify the problem: You want to understand why the minimum value of a function is not less than -2. 2. Typically, to find the minimum value of a function, we analyze its critical points by taking the derivative and setting it to zero. 3. Suppose the function is $f(x)$ and its minimum value is claimed to be $-2$. 4. The minimum value means $f(x) \geq -2$ for all $x$ in the domain. 5. To verify this, we can check the function's behavior at critical points and endpoints. 6. If the function is continuous and differentiable, and the minimum is $-2$, then $f(x) + 2 \geq 0$ for all $x$. 7. This implies the function never goes below $-2$. 8. Without the original function, the general reasoning is that the minimum value is the lowest point on the graph, so if it is $-2$, the function's values are always greater than or equal to $-2$. 9. If you provide the original function, I can show detailed steps to find and confirm the minimum value.