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

question 51

Short Answer

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

---

Definitions:

Gatekeeper

An individual or entity that controls access to something, often used in the context of deciding who gets access to information, resources, or areas within organizations.

Informant

A person who provides valuable information or insights about a specific group, culture, or phenomenon for research purposes.

Bargainer

An individual or entity engaged in negotiation or bargaining to reach mutually beneficial agreements or resolve disagreements.

Ethnographer Entered

A situation in which an ethnographer enters a community or field setting to conduct observational research.