A Function F Is Given, and the Indicated Transformations Are $f ( x ) = | x |$

question 30

Essay

A function f is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. $f ( x ) = | x |$
; shift to the left $\frac { 1 } { 2 }$
unit, shrink vertically by a factor of 0.2, and shift downward 2 units.

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Definitions:

Standard Deviation

A metric for assessing how much the data points differ or spread out in a collection of values.

Observations

Individual data points or recorded values from an experiment or study.

Geometric Mean

A type of mean or average, which indicates the central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum).

Weighted Mean

The mean of a data set that accounts for the importance or weight of each value.