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 5

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:

Manipulative Behaviour

Actions aimed at influencing or controlling others' actions or feelings through deceptive or indirect means, often for personal gain.

Social Charm

The ability to attract and influence others through one's personality, appearance, or behavior, fostering positive social interactions and relationships.

Excessive Guilt

A psychological condition where an individual experiences an overly intense feeling of responsibility or remorse for an action, often disproportionate to the actual situation.

Vulnerability Model

A theory suggesting that individuals have differing levels of vulnerability to stress and mental illness due to genetic, psychological, or environmental factors.