Give a Rule for the Piecewise-Defined Function $f ( x ) = \left\{ \begin{array} { l l } x - 3 & \text { if } x \neq 3 \\ - 2 & \text { if } x = 3 \end{array} ; \right.$

question 473

Multiple Choice

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

• A) \(f ( x ) = \left\{ \begin{array} { l l } x - 3 & \text { if } x \neq 3 \\ - 2 & \text { if } x = 3 \end{array} ; \right.\) Domain: \(( - \infty , \infty )\), Range: \(( - \infty , 3 ] \cup [ 3 , \infty )\)
• B) \(f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x \neq 3 \\ - 2 & \text { if } x = 3 \end{array} ; \right.\) Domain: \(( - \infty , \infty )\), Range: \(( - \infty , 3 ) \cup ( 3 , \infty )\)
• C) \(f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x \neq 3 \\ - 3 & \text { if } x = 3 \end{array} ; \right.\) Domain: \(( - \infty , 3 ] \cup [ 3 , \infty )\), Range: \(( - \infty , \infty )\)
• D) \(f ( x ) = \left\{ \begin{array} { l l } 2 x - 3 & \text { if } x < 3 \\ 2 x + 3 & \text { if } x \geq 3 \end{array} ; \right.\) Domain: \(( - \infty , 3 ) \cup ( 3 , \infty )\), Range: \(( - \infty , \infty )\)

---

Definitions:

Bad Living Situations

Conditions or environments where housing, safety, or hygiene standards are poor and negatively impact the well-being of residents.

Traditional Woman

A term that may refer to women adhering to conventional roles often associated with domestic responsibilities and caregiving.

Sensible Hobby

Refers to a leisure activity chosen wisely that is both enjoyable and beneficial to personal development or health.

Positive Processing

Cognitive activities oriented towards and emphasizing positive aspects of a situation or experience.