Problem 134 - Precalculus Essentials

Question

What must be done to a function's equation so that its graph is shrunk horizontally?

Step-by-Step Solution

Answer

To make a function's graph shrink horizontally, the x-values in the function's equation should be multiplied by a factor greater than 1. This implies transforming the function from \(y=f(x)\) to \(y=f(bx)\), with \(b\) greater than 1.

Step 1: Understand function transformations

Function transformations mean shifting or distorting the graph of a function in some fashion. Adjustments to a function's equation can result in its graph being shifted, reflected or 'stretched/shrunken' along the x or y axis.

Step 2: Recognize what a horizontal shrink represents

A horizontal shrink (also called horizontal compression) of a function's graph means that the graph is 'squeezed' horizontally toward the y-axis.

Step 3: Determine the equation alteration for horizontal shrink

To shrink a function's graph horizontally, the x-values of the function should be multiplied by a factor greater than 1. In the equation of a function, if \(y=f(x)\) is the original function, to shrink it horizontally, the function would need to be transformed into \(y=f(bx)\), where \(b\) is greater than 1.