y=af(x), 0
In the given equation, y = af(x), where 0 < a < 1, we have a function f(x) being scaled or stretched by a factor of a
In the given equation, y = af(x), where 0 < a < 1, we have a function f(x) being scaled or stretched by a factor of a
In the given equation, y = af(x), where 0 < a < 1, we have a function f(x) being scaled or stretched by a factor of a. To better understand this, let's break down the components of the equation. - f(x) represents the original function, where x is the input and f(x) is the output. - a is the scaling factor, which determines the amount of stretching or shrinking applied to the function. - y represents the output of the scaled function. When a < 1, it means that the scaling factor is less than 1. This implies that the function is being shrunk or compressed vertically. If a > 1, the function would be stretched vertically.
Here’s an example to illustrate this concept further:
Let’s assume f(x) = x^2, and a = 0.5.
If we apply the scaling factor to the function, y = 0.5f(x), it becomes y = 0.5(x^2). This means that the original parabola would be compressed vertically, leading to a narrower shape.
For example, if we plot both f(x) = x^2 (original function) and y = 0.5(x^2) (scaled function), we would observe that the scaled function’s y-values are halved compared to the original function.
Thus, by multiplying the original function by a scaling factor less than 1, we effectively shrink the function vertically.
More Answers:
Unlock the Power of Variable Multiplication in Math: Understanding the Equation y = af(x) with a > 1Understanding the Equation Y = f(x) – d: Components and Applications
Understanding the Equation: Horizontal Shift of a Basic Function and Its Interpretation