What is the effect of a horizontal compression on the graph of a function?

A horizontal compression of a function graphically affects the spacing of the points along the x-axis. When a function undergoes a horizontal compression, the output values (y-values) remain the same, but the input values (x-values) are scaled down. This means that for a given y-value, the corresponding x-value becomes smaller, resulting in the graph appearing narrower.

For example, if we take a function f(x) and compress it horizontally by a factor of k (where k > 1), the new function can be represented as f(x/k). This transformation effectively pulls the curve closer together along the x-axis, which is why we describe it as getting narrower. The original distances between the points of the graph along the x-axis become smaller, resulting in the 'narrowing' effect.

This understanding is important to visualize how functions behave under transformations, which can be crucial for graphing and analyzing functions in calculus and algebra.