What does f(Bx) represent in terms of graph transformation?

The expression f(Bx) indicates a transformation of the function f(x) based on the value of B. When B is greater than 1, the argument Bx results in a horizontal squeeze of the graph. This means that the graph of f(x) is compressed towards the y-axis, causing the x-coordinates of points on the graph to scale down. Conversely, if B is a fraction between 0 and 1, the graph undergoes a horizontal stretch, expanding away from the y-axis.

To elaborate on this further, when you input Bx into the function f, you are effectively controlling the rate at which the function operates along the horizontal axis. For instance, if B is 2, then for each x-value, the output corresponds to f(2x). To reach the same output that f(x) would provide, you now need to multiply the input x by a factor of 2, thereby squeezing the function graph horizontally.

This transformation is distinct from a vertical shift, which would move the graph up or down without altering its width. Similarly, a reflection across the x-axis would invert the function vertically, and a horizontal shift would move the entire graph left or right without changing its shape. Therefore, the transformation represented