vertical shrink
Vertical shrink refers to the compression or reduction of the vertical size or distance of a graph or shape
Vertical shrink refers to the compression or reduction of the vertical size or distance of a graph or shape. It is a transformation that can be applied to functions, graphs, or objects in mathematics.
When a graph or shape is vertically shrunk, all the y-values or heights of the graph or shape are scaled down. This means that the graph or shape appears shorter in the vertical direction compared to its original size, while the horizontal position of the points remains unchanged.
To achieve a vertical shrink, a scaling factor is used. This scaling factor is a positive number less than 1, representing the degree of compression or reduction. Let’s call this scaling factor “k”. When the scaling factor “k” is multiplied by all the y-values of the graph or shape, it results in the vertically shrunk graph or shape.
To understand this concept, consider the function y = f(x). A vertical shrink could be represented as y = k * f(x), where “k” is the scaling factor.
For example, let’s say we have the function y = 2x. If we want to vertically shrink this function by a factor of 0.5, we multiply the original function by 0.5:
y = 0.5 * 2x
y = x
This means that all the y-values of the original function have been halved, resulting in a vertically shrunk graph. The horizontal positions of the points on the graph remain the same.
In graphs, a vertical shrink can be observed as the graph appearing “squashed” vertically, with the y-values compressed or reduced. The degree of shrinkage depends on the value of the scaling factor “k”. The closer the value of “k” is to 0, the greater the compression or shrinkage.
It is worth noting that a vertical shrink does not affect the x-values or the horizontal position of the points. Only the y-values are compressed or reduced. Additionally, a scaling factor greater than 1 would result in a vertical stretch instead of a vertical shrink.
Overall, a vertical shrink is a transformation that compresses or reduces the height or vertical size of a graph or shape, achieved by multiplying the y-values by a scaling factor “k” less than 1.
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