Consider the Following Function $$f ( x ) = \left\{ \begin{array} { c c } 3 - x & x < - 1 \\x & - 1 \leq x < 3 \\( x - 3 ) ^ { 2 } & x \geq 3\end{array} \right.$$

question 79

Short Answer

Consider the following function. $$f ( x ) = \left\{ \begin{array} { c c } 3 - x & x < - 1 \\x & - 1 \leq x < 3 \\( x - 3 ) ^ { 2 } & x \geq 3\end{array} \right.$$
Determine the values of $a$ for which $\lim _ { x \rightarrow a } f ( x )$ exists.

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Definitions:

Transactional Analysis

A psychotherapeutic approach that views interactions between individuals as transactions and uses these to understand and improve communication and behavior.

Therapeutic Relationship

The dynamic and collaborative interaction between therapist and client, pivotal in facilitating change and healing in therapy.

Ego State

A concept in psychology that refers to one of the three parts of the personality structure in Freud's psychoanalytic theory, characterized as the realistic part that mediates between the desires of the id and the morals of the superego.

Game

A structured form of play or competitive activity, often undertaken for enjoyment and sometimes used as a tool in therapy to address psychological issues.