Write an Equation for the Function That Is Described by the Given

question 21

Multiple Choice

Write an equation for the function that is described by the given characteristics. A sine curve with a period of $4 \pi$ , an amplitude of 8 , a left phase shift of $\frac { \pi } { 4 }$ , and a vertical translation down 1 unit.

• A)\(y = 8 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) - 1\)
• B)\(y = 1 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) - 8\)
• C) \(y = 8 \sin \left( \frac { x } { 2 } + \pi \right) - 1\)
• D) \(y = 8 \sin \left( x + \frac { \pi } { 2 } \right) - 1\)
• E) \(y = 8 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) + 1\)

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Definitions:

Medium

A means or channel of communication, such as television, radio, print, or digital platforms, through which information or messages are conveyed.

Economical

Pertaining to efficient and prudent use of resources, ensuring minimal waste and maximum value.

Planning Phase

The initial stage in a project or process where objectives are defined and strategies are developed.

Analyzing

The process of examining something in detail in order to understand it better or to draw conclusions from it.