The Graph of a Piecewise-Defined Function Is Given $f ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { 2 } x & \text { if } - 4 < x < 0 \\ x & \text { if } 0 < x < 3 \end{array} \right.$

question 264

Multiple Choice

The graph of a piecewise-defined function is given. Write a definition for the function.
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• A) \(f ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { 2 } x & \text { if } - 4 < x < 0 \\ x & \text { if } 0 < x < 3 \end{array} \right.\)
• B) \(f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } - 4 \leq x \leq 0 \\ x & \text { if } 0 < x \leq 3 \end{array} \right.\)
• C) \(f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x & \text { if } - 4 < x < 0 \\ x & \text { if } 0 < x < 3 \end{array} \right.\)
• D) \(f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x & \text { if } - 4 \leq x \leq 0 \\ x & \text { if } 0 < x \leq 3 \end{array} \right.\)

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Definitions:

Social Interaction

The process by which individuals act and react to those around them, forming the basis of relationships and societal structure.

Sense of Self

The evolving perception an individual has about themselves, encompassing self-awareness, self-image, and self-esteem.

Negative Emotions

Feelings that are generally perceived as being unpleasant or harmful, such as sadness, anger, fear, or jealousy.

Emotional Well-being

The general state of being comfortable, healthy, or happy, but more specifically relating to the emotional quality and depth of an individual's life.