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

question 106

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:

PhOH

Phenol, an aromatic compound with the formula C6H5OH, known for its antiseptic properties.

Reactive Intermediate

A reactive intermediate is a short-lived, high-energy molecule formed during the conversion of reactants into products in a chemical reaction.

Addition Polymers

Polymers formed by the sequential addition of monomers without the loss of any molecule.

Step-growth

A polymerization process where chains grow by the stepwise reaction between functional groups, leading to high molecular weight polymers.