Which compound inequality shows the range of a scale factor that would produce a reduction or shrinking of a preimage? Enter the number of the correct option.

Question

Option #1: −1≤x≤0−1≤x≤0
Option #2: 1>x≥21>x≥2
Option #3: 0<x<10<x<1
Option #4: −1≤x≤1−1≤x≤1

Answer 1

To determine the range of a scale factor that would produce a reduction or shrinking of a preimage, we need to consider how scale factors work.

A scale factor less than 1 but greater than 0 will shrink the image. Additionally, a negative scale factor will also produce a reflection and potentially a shrinking effect, but specifically for the purpose of reduction (shrinking without the complication of reflections), we are interested in scale factors between 0 and 1.

Therefore, the correct compound inequality for a scale factor that produces a reduction or shrinking of a preimage is:

Option #3: \(0 < x < 1\)

This indicates that the scale factor \(x\) must be a positive number less than 1 to achieve the desired shrinking effect.