Provide an Appropriate Response $\mathrm { f }$ To See Whether It Appears to Have a Continuous Extension

question 41

Multiple Choice

Provide an appropriate response.
-Use a calculator to graph the function $\mathrm { f }$ to see whether it appears to have a continuous extension to the origin. I it does, use Trace and Zoom to find a good candidate for the extended function's value at $x = 0$ . If the function does not appear to have a continuous extension, can it be extended to be continuous at the origin from the right the left? If so, what do you think the extended function's value(s) should be?
$f ( x ) = \frac { 4 \sin x } { | x | }$

• A) continuous extension exists at origin; f(0) = 0
• B) continuous extension exists from the right; f(0) = 1 continuous extension exists from the left; f(0) = -1
• C) continuous extension exists at origin; f(0) = 4
• D) continuous extension exists from the right; f(0) = 4 continuous extension exists from the left; f(0) = -4

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Definitions:

Temporal Bone

A pair of bones forming part of the side of the skull, housing structures of the ear and contributing to the cranial cavity's protection.

Ethmoid Bone

A spongy bone located between the eyes that contributes to the medial walls of the orbits, the roof of the nasal cavity, and the nasal septum.

Epiphysis

The expanded end of a long bone.

Medullary Cavity

The central cavity of bone shafts where red and yellow bone marrow is stored.