Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value Function
The absolute value function, denoted as f(x) = |x|, outputs the non-negative value of x. This function is V-shaped, with its vertex at the origin (0,0), and it reflects any negative input to positive output. Understanding this function is crucial for graphing transformations, as it serves as the base graph for modifications.
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Transformations of Functions
Transformations involve altering the graph of a function through shifts, stretches, compressions, or reflections. For example, the function r(x) = (1/2) |x + 2| represents a vertical compression by a factor of 1/2 and a horizontal shift left by 2 units. Mastery of these transformations allows for accurate graphing of modified functions based on the original absolute value function.
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Domain & Range of Transformed Functions
Graphing Techniques
Graphing techniques include plotting key points, identifying transformations, and understanding the behavior of functions. For the function r(x), one would start by graphing f(x) = |x|, then apply the transformations to find the new vertex and shape. Effective graphing techniques are essential for visualizing and interpreting the behavior of functions in algebra.
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