Graph the Function $\mathrm { f } ( \mathrm { x } ) = - \tan \mathrm { x }$

question 246

Essay

Graph the function $\mathrm { f } ( \mathrm { x } ) = - \tan \mathrm { x }$ on the interval $\left( - \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right)$ . Explain why it is correct to say that $\mathrm { f }$ is decreasing on the interval $\left( \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right)$ , but it is incorrect to say that $\mathrm { f }$ is decreasing on the interval $\left( - \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right)$ .

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Definitions:

IR

Infrared spectroscopy, a technique used to identify and study chemicals through the absorption of infrared radiation, providing insights into molecular vibrations and structures.

NMR

Nuclear Magnetic Resonance, a spectroscopic technique that provides detailed information about the structure, dynamics, and environment of molecules.

Type I Error

The mistake of rejecting a true null hypothesis in hypothesis testing, also known as a "false positive."

Type II Error

A statistical error that occurs when a false null hypothesis is not rejected, indicating a false negative finding in testing.