For the Function $y = \frac { 2 ^ { 2 / x } } { x }$

question 30

Essay

For the function $y = \frac { 2 ^ { 2 / x } } { x }$ , ( $x < 0$ ), use a graphing calculator to find, correct to two decimal places,
(a) the intervals on which the function is increasing or decreasing, and
(b) the range of the function.

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Definitions:

Mitochondria

Membrane-bound organelles found in the cytoplasm of eukaryotic cells, vital for energy production through cellular respiration.

Cell Walls

Rigid or semi-rigid structures surrounding the cell membrane of some cells, providing structural support and protection.

Capsules

Structures that enclose certain organisms or parts of organisms, often for protection, such as bacterial capsules which help evade immune responses.

Bacterial Membrane

The lipid bilayer surrounding a bacterium, controlling the movement of substances in and out of the cell.