Understanding Scaling Factors in Mathematical Transformations

y=af(x), 0

This equation represents a transformation of the function f(x) by a scaling factor a

This equation represents a transformation of the function f(x) by a scaling factor a. When a is between 0 and 1, it means that the output values of f(x) will be scaled down or reduced.

To understand this, let’s consider an example. Suppose we have the function f(x) = x^2, and we want to find the equation of y = af(x) where a = 0.5.

We first calculate f(x) by substituting x^2 into the equation:
f(x) = x^2

Now, we apply the scaling factor by multiplying f(x) by a:
y = 0.5 * (x^2)

So, the equation y = 0.5x^2 represents the transformation of the function f(x) = x^2, where each y-value in the transformed function is half of the corresponding y-value in the original function.

This means that for any x-value we choose, the y-value in the transformed function will be half as large compared to the original function.

In general, when 0 < a < 1, the function f(x) is scaled down, making the values of y smaller compared to f(x) for the same x-values. Each y-value is multiplied by a, resulting in a decrease in magnitude. This is why the graph of y = af(x) will be "squeezed" closer to the x-axis compared to the graph of f(x).

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