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:

Coccyx

A small, triangular-shaped bone consisting of three to five fused vertebrae.

Vertebrae

The individual bones that make up the vertebral column (spine), providing structural support and protecting the spinal cord.

Hip Bones

Large bones that form the foundation of the pelvis, playing a crucial role in supporting the body's weight and facilitating movement.

Pelvic Organs

The internal organs within the pelvic region of the body, including the bladder, rectum, and, for females, the uterus and ovaries.