Understanding Vertical Stretch in Mathematics: Explained and Demonstrated

vertical stretch

In mathematics, a vertical stretch is a transformation that changes the size of a graph or function in the vertical direction

In mathematics, a vertical stretch is a transformation that changes the size of a graph or function in the vertical direction. It stretches or compresses the graph or function vertically, making it taller or shorter.

To understand how a vertical stretch works, let’s consider a simple example. Consider the function f(x) = x^2, which is a basic parabola. If we apply a vertical stretch to this function, it will result in a new function, let’s call it g(x).

The general form of a vertical stretch can be represented as y = a * f(x), where ‘a’ is a positive constant. Let’s say we want to stretch the function f(x) vertically by a factor of 2. This means that we want to make the graph double the height. Therefore, our new function g(x) will be g(x) = 2 * f(x).

To graphically understand the effect of this vertical stretch, let’s look at a few points:

For example, for the original function f(x) = x^2, if we evaluate it at x = 1, we get f(1) = 1^2 = 1. This corresponds to the point (1, 1) on the graph of f(x).

Now, let’s find the corresponding point on the stretched graph g(x). Plugging x = 1 into g(x) = 2 * f(x), we get g(1) = 2 * f(1) = 2 * 1 = 2. So, the point (1, 2) is on the graph of g(x).

You can graph more points in the same manner and observe how the stretched graph changes. You will always find that the y-values on the stretched graph are double the y-values on the original graph.

So, in general, a vertical stretch multiplies the y-values of a function or graph by a positive constant ‘a’, making it taller or shorter depending on the value of ‘a’. If ‘a’ is greater than 1, it results in a stretch, while if ‘a’ is between 0 and 1, it results in a compression.

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