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:

Flatworms

A group of invertebrates belonging to the phylum Platyhelminthes, characterized by their flattened bodies, bilateral symmetry, and lack of body cavity.

Anus

The opening at the end of the digestive tract through which feces exit the body.

Premolars

In mammals, teeth positioned between the canines and molars; adapted for crushing and grinding; compare with incisors, canines, and molars.

Incisors

Chisel-shaped teeth of a mammal; adapted for biting and cutting food. Compare with canines, premolars, and molars.