IP331.com | Online Tools

Algebra Tools Geometry Tools Trigonometry Tools Matrix Tools Function Tools Number Theory Tools Base Converter Electronics & Physics Statistics Tools Life & Finance

Home›Function Tools›Function Compression Calculator

Function Compression Calculator

Apply vertical and horizontal compressions (0<factor<1) to functions

Select Type

Vertical Linear Horizontal Linear Vertical Quadratic Horizontal Quadratic

f(x)=x+, compress by

Compression Rules

Vertical compression by a (0<a<1): g(x)=a*f(x)

Horizontal compression by a: g(x)=f(x/a)

Compression = reciprocal of stretch

Equivalent to stretch by 1/a

Compression is the opposite of stretch. A compression factor between 0 and 1 squashes the graph toward the axes. Vertical compression flattens, horizontal compression narrows. Compression and stretch are reciprocal transformations.

⚠ Compression factor must be between 0 and 1. Factor > 1 would be a stretch. Compression by a = stretch by 1/a.

What Is a Function Compression?

A compression reduces the vertical or horizontal size of a graph. Mathematically, it multiplies the output (vertical) by a factor 0<a<1 or divides the input (horizontal) by a factor 0<a<1. Compression is the reciprocal of stretching.

Vertical Compression

g(x)=a*f(x), 0<a<1. Flattens graph. Slope reduced. x-intercepts fixed.

Horizontal Compression

g(x)=f(x/a), 0<a<1. Narrows graph. Slope increased. y-intercept fixed.

Relation to Stretch

Compression by a = stretch by 1/a. Example: compress by 1/3 = stretch by 3.

Key Points

Origin stays fixed. Intercepts on the scaled axis stay fixed. Other points move toward the axis.

Teaching Example: f(x)=4x+2, vertical compress by 0.5. g(x)=0.5*(4x+2)=2x+1. Slope halves from 4 to 2. y-intercept halves from 2 to 1.

Applications

Graphing Amplitude Control Signal Processing Data Normalization Audio Engineering

Frequently Asked Questions

What is compression?▼

Multiply output (vertical) or divide input (horizontal) by 0<a<1. Squashes the graph.

Compression vs stretch?▼

Same operation, different factor range. Compress by a = stretch by 1/a. a<1 compresses, a>1 stretches.

Effect on slope?▼

Vertical compression: slope reduced (flatter). Horizontal compression: slope increased (steeper).

Does origin move?▼

No, origin (0,0) stays fixed. Both vertical and horizontal compressions preserve the origin.

More Function Tools

Taylor Series Calculator

Compute Taylor series expansion around a center point up to n terms

›

Composite Function Evaluator

Evaluate f(g(x)) numerically at a given x value step by step

›

Asymptote Finder

Find vertical and horizontal asymptotes of rational functions

›

Discontinuity Classifier

Classify discontinuities as removable, jump, or infinite

›

Maclaurin Series Calculator

Expand functions in Maclaurin series (Taylor at x=0)

›

Logistic Function Analyzer

Analyze S-curve logistic functions with carrying capacity and inflection point

›