For What Value of the Constant $c$ Is the Function $f$ Continuous On

question 56

Multiple Choice

For what value of the constant $c$ is the function $f$ continuous on $( - \infty , \infty ) ?$
$f ( x ) = \left\{ \begin{array} { l l l } c x + 5 & \text { for } & x \leq 2 \\ c x ^ { 2 } - 5 & \text { for } & x > 2 \end{array} \right.$
Select the correct answer.

• A) \(c = 1\)
• B) \(c = 5\)
• C) \(c = - 2\)
• D) \(c = - 5\)
• E) \(c = 2\)

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Definitions:

Heuristics

Cognitive shortcuts or rules of thumb that simplify decision making by reducing complex problem-solving to simpler judgment processes.

Ethical implications

The moral consequences or considerations arising from actions, decisions, or policies in personal, professional, or organizational contexts.

Decision entrapment

A situation where individuals continue to invest in a decision despite new evidence suggesting it may have been the wrong choice.

Satisficing

A decision-making strategy that involves selecting an acceptable or adequate solution, rather than the optimal one.