At What Value(s) of X Is the Function

question 30

Essay

At what value(s) of x is the function $$f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } + 4 x + 5 & \text { if } x < - 2 \\\frac { 1 } { 2 } x & \text { if } - 2 \leq x \leq 2 \\1 + \sqrt { x - 2 } & \text { if } x > 2\end{array} \right.$$

---

Definitions:

Functional Autonomy

A concept in psychology where a behavior continues because it is intrinsically rewarding, despite the original motives or goals being absent or changed.

Erratic Toilet Training

Inconsistent approaches to potty training a child, which may lead to confusion and difficulties in learning proper bathroom habits.

Sadism

A psychological condition where individuals derive pleasure from inflicting pain or suffering on others.

Chauvinism

An exaggerated or aggressive patriotism or blind enthusiasm for military glory; alternatively, it can refer to biased devotion to any cause, group, or gender.