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

---

Definitions:

Automatic Process

Cognitive processes that occur with little to no conscious thought or effort, often developed through repetition and practice.

Controlled Process

A type of cognitive processing that requires conscious, intentional, and effortful attention and thought.

Knitting

is the craft of creating fabric by interlocking loops of yarn with needles, often resulting in items like sweaters, hats, and scarves.

Automatic Processing

A type of cognitive processing that occurs with little to no conscious effort, allowing for tasks to be performed quickly and efficiently.