Horizontal and vertical scaling

Horizontal and vertical scaling of functions

Understand how multiplying a function output differs from multiplying its input. This precalculus practice set develops coordinate reasoning for stretches, compressions and reflections, with special attention to the reciprocal relationship between an inside factor and horizontal distances.

Start by identifying whether a factor affects height or width. Then map individual points, transform domains and ranges, and recover factors from a known original-to-transformed correspondence. Negative factors introduce reflections that must be combined with the change in magnitude. A time-based example connects horizontal scaling with a process that runs faster.

Prerequisites are function notation, interval notation, translations and axis reflections. Before selecting a response, write an equation matching the transformed argument to the original input. Check an output separately rather than applying one factor to both coordinates.

The questions include single-select and multiselect formats with explanations of tempting stretch-versus-compression errors. Later items examine when different scaling descriptions can represent the same graph and why a zero factor cannot be handled by an invertible coordinate map. Difficulty progresses through interpretation, computation, reconstruction and justification. General shifted-and-scaled parameter reconstruction belongs to the following set.