Translation of "Graph strecken und stauchen" in English

The translation of "Graph strecken und stauchen" into English is "stretching and compressing the graph."

To stretch a graph means to elongate it either horizontally or vertically. This is done by multiplying the x or y-coordinates of the points on the graph by a constant factor. Stretching horizontally increases the spacing between the points, making the graph wider or narrower, while stretching vertically increases the distance between the points, making the graph taller or shorter.

On the other hand to compress a graph means to condense it either horizontally or vertically. This is done by dividing the x or y-coordinates of the points on the graph by a constant factor. Compressing horizontally decreases the spacing between the points, making the graph narrower or wider, while compressing vertically decreases the distance between the points, making the graph shorter or taller.

In mathematical terms stretching and compressing a graph involves applying a transformation to the original function. The transformation function can be written as:

f(x) = a * g(b(x - c)) + d

where a, b, c, and d are constants that determine the amount and direction of the stretch or compression. The constant a controls the vertical scaling b controls the horizontal scaling c determines the horizontal shift, and d determines the vertical shift.

For example, if we have the function f(x) = x^2 and we want to stretch the graph vertically by a factor of 2, the transformation function would be f(x) = 2 * x^2. This would result in a graph that is twice as tall as the original.

Similarly, if we want to compress the graph horizontally by a factor of 0․5, the transformation function would be f(x) = (0.5 * x)^2. This would result in a graph that is half as wide as the original.

In conclusion, when translating "Graph strecken und stauchen" into English, the appropriate terms are "stretching and compressing the graph." These transformations involve either elongating or condensing the graph either horizontally or vertically by applying specific scaling and shifting factors to the original function.