The Graph of a Piecewise-Defined Function Is Given $f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \\ \frac { 1 } { 2 } x & \text { if } 3 < x \leq 5 \end{array} \right.$

question 9

Multiple Choice

The graph of a piecewise-defined function is given. Write a definition for the function.
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• A) \(f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \\ \frac { 1 } { 2 } x & \text { if } 3 < x \leq 5 \end{array} \right.\)
• B) \(f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \\ \frac { 1 } { 2 } x + \frac { 1 } { 2 } & \text { if } 3 < x \leq 5 \end{array} \right.\)
• C) \(f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \\ \frac { 1 } { 2 } x + 2 & \text { if } 3 < x \leq 5 \end{array} \right.\)
• D) \(f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \\ \frac { 1 } { 2 } x - \frac { 1 } { 2 } & \text { if } 3 < x \leq 5 \end{array} \right.\)

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Definitions:

Participant Observation

A qualitative research method in which the researcher immerses themselves in the environment they are studying, participating in the activities while observing the setting and individuals within it.

Validation

The process of confirming or verifying something as true, correct, or compliant with standards.

Surveying

The science of measuring land to determine its boundaries, area, and the physical features it encompasses.

Premature Closure

The tendency to make a decision or come to a conclusion before acquiring all relevant information.