9-24 Graph the function by hand, not by plotting points, but...

$9-24$ Graph the function by hand, not by plotting points, but by
starting with the graph of one of the standard functions given in Sec-
tion $1.2,$ and then applying the appropriate transformations.
$$y=|\sin x|$$

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Key Concepts

Function Transformations

This concept involves applying operations to basic functions in order to obtain new functions without plotting individual points. It includes moves such as reflections, translations, stretches, and compressions, which help in understanding and quickly sketching the graph of the transformed function by relating it to a standard function graph.

Absolute Value Transformation

The absolute value operation affects a function by taking every output value and replacing it with its non-negative counterpart. Graphically, this means that portions of the original function that fall below the x-axis are reflected above the axis, turning negative values into positive ones. This is key when graphing functions like |sin x|, where the sine function’s negative segments are flipped upward.

Standard Trigonometric Functions

Standard trigonometric functions, such as the sine function, have well-known graphs with regular periodic behavior. Understanding their baseline properties, including period, amplitude, and symmetry, is crucial before applying transformations. This provides a starting point from which transformations like the absolute value operation can be applied.

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