y=f(bx), b>1
In mathematics, the given equation y = f(bx) represents a function that relates the variable y to the variable bx, where b is a constant greater than 1
In mathematics, the given equation y = f(bx) represents a function that relates the variable y to the variable bx, where b is a constant greater than 1. This equation can be seen as a transformation of the function f(x), where the input x is multiplied by the constant b.
The effect of multiplying the input by b in this equation can be summarized as follows:
1. Stretching: When b is greater than 1, the input values of the function f(x) are multiplied by a factor greater than 1. This results in the function being stretched horizontally compared to the original f(x) graph. The stretching factor is determined by the value of b.
2. Compression: Alternatively, if b is a fraction between 0 and 1, the input values are multiplied by a factor less than 1. This compresses the function f(x) horizontally, making it narrower than the original graph.
3. Scaling: The vertical axis of the graph remains unchanged, as it is represented by the function f(x). Only the input values, bx, undergo the transformation.
It is important to note that without knowing the specific function f(x), we cannot provide further details on the nature of the transformation or on the behavior of the graph. However, the general understanding of the transformation described above can be applied to better understand the effect of multiplying the input by b.
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