Question

The function grabbed with a solid line is apparent function y equals f of x which of the following you describe and describes the transformation function y equals 4 f of x which is shown with the dotted line

Answer 1

The transformation of the function \( y = f(x) \) to \( y = 4f(x) \) represents a vertical scaling of the original function. Specifically, multiplying the function \( f(x) \) by 4 means that every output (or value of \( y \)) of the original function is stretched vertically by a factor of 4.

Here's how to describe the transformation:

1. **Vertical Stretch**: The dotted line represents a vertical stretch of the original function. Each value of \( f(x) \) is multiplied by 4, causing the peaks and valleys of the graph to rise or fall to four times their original heights.

2. **No Horizontal Shift**: The transformation does not affect the x-values; the graph retains its original x-coordinates.

Thus, the dotted line shows a vertical stretch of the original function \( y = f(x) \) by a factor of 4, with no shifts in the horizontal direction.