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:

Column Variable

A variable whose values are laid out in columns in a table or dataset, facilitating vertical comparison across data points.

Alpha

In statistics, alpha often denotes the level of significance, a threshold below which the null hypothesis is rejected.

Chi-Square

A statistical test used to determine if a significant relationship exists between two categorical variables in a contingency table.

Degrees of Freedom (df)

Number of values or quantities free to vary when a statistic is used to estimate a parameter.