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

Understand the factors contributing to political democracy and its challenges.

Analyze the role of political parties, lobbies, and other political organizations in shaping policies and governance.

Understand the relationship between economic power and political influence.

Understand the mechanisms through which citizens can influence or control the state in modern democracies.

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Definitions:

Ether

A class of organic compounds characterized by an oxygen atom connected to two alkyl or aryl groups, used as solvents and in chemical synthesis.

Tertiary Amine

An amine where the nitrogen atom is connected to three alkyl or aryl groups.

Ethanol

Ethanol, also known as ethyl alcohol, is a volatile, flammable, colorless liquid commonly used as a psychoactive drug in alcoholic beverages and as a solvent in the chemical industry.

Metabolic Oxidation

The process in which organic substances are broken down to produce energy in cells.