Final answer:
A horizontal stretch with |c| < 1 widens the graph horizontally, causing the points to spread out more along the x-axis except for points on the y-axis itself.
Step-by-step explanation:
When a function's graph undergoes a horizontal stretch with a factor of |c| < 1, the result is that the graph widens horizontally. This type of transformation affects the spacing between points on the graph; points that were once at a certain distance from the y-axis are now further away, except for points on the y-axis itself. This horizontal stretch makes the graph appear more spread out along the x-axis.
For example, if the original function is f(x) and the transformed function is f(cx), with |c| being less than 1 but greater than 0, every point (x, y) on the graph of f(x) will be mapped to a new point (x/c, y) on the graph of f(cx). If we consider a simple function like y = f(x) = x, and apply a horizontal stretch by a factor of 0.5, we would get the new function y = f(0.5x), which appears wider than y = x because each x-coordinate is halved, hence points are twice as far apart on the x-axis.