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 $( - \infty , \infty ) ?$
$$f ( x ) = \left\{ \begin{array} { l l l } c x + 5 & \text { for } & x \leq 2 \\c x ^ { 2 } - 5 & \text { for } x > 2\end{array} \right.$$

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Definitions:

Endometrium

The mucous membrane lining the interior of the uterus, which thickens during the menstrual cycle to prepare for potential pregnancy.

Uterus

The uterus is a significant female reproductive organ in many mammals, including humans, where it serves as the site for fetal development during pregnancy.

Interstitial Cells

Cells located in the spaces between other cells in a tissue or organ, often involved in hormone production.

Testes

The male reproductive organs that produce sperm and hormones, primarily testosterone.