horizontal compression
[horizontal compression|horizontal compression] refers to a horizontal compression by a factor of 1 5 of the graph of f.
Definition
horizontal compression refers to a horizontal compression by a factor of 1 5 of the graph of f. Starting with horizontal transformations, f ( 3 x ) represents a horizontal compression by 1 3. This transformation involves multiplying each x-value by 1 3, which alters the graph's scale horizontally.
Mechanism
horizontal compression The graph of y = (2x)^2 represents a horizontal compression of y = x^2 by a factor of 1/2. This transformation stretches the graph horizontally when the coefficient inside the function is greater than 1. Conversely, a horizontal stretch occurs when the coefficient is between 0 and 1. The factor determines the degree of compression or stretch applied to the graph. Horizontal compression or stretch alters the graph's shape while maintaining its overall structure.
Effects
horizontal compression causes input values to be half their original distance from the vertical axis, resulting in a horizontal compression effect on the graph. This transformation occurs when a constant greater than 1 is multiplied by the input. The effect alters the graph's scale without changing the vertical axis values. The compression affects how input values are mapped to the graph's horizontal axis. The transformation maintains the original vertical positions while compressing the horizontal spread.
Comparison
horizontal compression Horizontal compression occurs when | B | > 1 , resulting in a period less than 2 π . Whereas horizontal stretch happens when | B | < 1 , leading to a period greater than 2 π . The function undergoes horizontal compression compared to a standard period of 2 π . This contrast highlights how changes in | B | affect the function's period and transformation direction .
Function Description Mechanism
horizontal compression involves modifying a function's graph by stretching or compressing it horizontally. This transformation is applied based on the given description of the function. The process requires sketching the original function's graph before applying the horizontal stretch or compression. The function's input values are scaled by a factor, which determines the extent of the compression or stretch. This mechanism alters the graph's shape while preserving its fundamental characteristics.
Horizontal Transformation
horizontal compression refers to a horizontal transformation where f(3x) indicates a compression by 1/3. This means each x-value is multiplied by 1/3. The transformation is defined by scaling the input values by a factor of 1/3.