Give a Rule for the Piecewise-Defined Function $f ( x ) = \left\{ \begin{array} { l l } 2 x & \text { if } x \leq 1 \\ x + 1 & \text { if } x > 1 \end{array} ; \right.$

question 465

Multiple Choice

Give a rule for the piecewise-defined function. Then give the domain and range.
-

• A) \(f ( x ) = \left\{ \begin{array} { l l } 2 x & \text { if } x \leq 1 \\ x + 1 & \text { if } x > 1 \end{array} ; \right.\) Domain: \(( - \infty , \infty )\), Range: \(( - \infty , \infty )\)
• B) \(f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } x \leq 1 \\ x + 1 & \text { if } x > 1 \end{array} \right.\); Domain: \(( - \infty , \infty )\), Range: \(( - \infty , \infty )\)
• C) \(f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } x \leq 1 \\ x + 2 & \text { if } x > 1 \end{array} \right.\); Domain: \(( - \infty , 2 ) \cup ( 2 , \infty )\), Range: \(( - \infty , \infty )\)
• D) \(f ( x ) = \left\{ \begin{array} { l l } - x & \text { if } x \leq 1 \\ 2 x + 1 & \text { if } x > 1 \end{array} ; \right.\) Domain: \(( - \infty , \infty )\), Range: \(( - \infty , 2 ) \cup ( 2 , \infty )\)

---

Definitions:

Virtue Ethics

An ethical theory that emphasizes the role of character and virtue in moral philosophy rather than either doing one’s duty or acting to bring about good consequences.

Stoic Frame

An approach to life based on stoicism, emphasizing rationality, personal virtue, and resilience in the face of adversity or emotional turmoil.

Ethical Dilemma

A situation in which a difficult choice has to be made between two or more morally correct actions that are in conflict.

Egoists

Individuals who are excessively focused on their own advantages, self-interests, and welfare, often at the expense of others.