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Home›Function Tools›Function Stretch Calculator

Function Stretch Calculator

Apply vertical and horizontal stretches to functions

Select Base Function and Stretch Type

Vertical Linear Horizontal Linear Vertical Quadratic Horizontal Quadratic

f(x)=x+, vertical stretch by

Stretch Rules

Vertical stretch by a: g(x) = a * f(x)

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

a > 1: stretch, 0 < a < 1: compression

Point (x,y) -> (x, a*y) vertical, (a*x, y) horiz

A stretch multiplies the output (vertical) or input (horizontal) by a factor. Stretching makes the graph taller or wider. Compression (factor between 0 and 1) squashes it. Key points transform predictably.

⚠ Stretch factor must be positive. Factor > 1 stretches, 0 < factor < 1 compresses. Negative factors also reflect.

What Is a Function Stretch?

Stretching a function multiplies the output (vertical stretch) or the input (horizontal stretch) by a constant factor. This changes the graph proportions while preserving the general shape. Vertical stretches affect the range, horizontal stretches affect the domain.

Vertical Stretch

g(x)=a*f(x). Multiply output by a. y-coordinates scaled. x-intercepts remain fixed.

Horizontal Stretch

g(x)=f(x/a). Divide input by a. x-coordinates scaled. y-intercepts remain fixed.

Stretch vs Compression

a>1: stretch (enlarges). 0<a<1: compression (shrinks). They are reciprocal transformations.

Combined Transformations

Stretches can be combined with shifts and reflections. Order matters: stretches first, then shifts.

Teaching Example: f(x)=2x+1, vertical stretch by 3. g(x)=3*(2x+1)=6x+3. Point (1,3) on f -> (1,9) on g. Slope tripled from 2 to 6.

Applications

Graphing Physics Signal Processing Amplitude Modulation Data Scaling

Frequently Asked Questions

Vertical vs horizontal stretch?▼

Vertical: multiply output. Horizontal: divide input. g(x)=a*f(x) vs g(x)=f(x/a).

Stretch vs compression?▼

Factor>1: stretch. 0<factor<1: compression. Stretch by 2 = compress by 1/2 (reciprocal).

Does stretch affect intercepts?▼

Vertical: x-intercepts unchanged, y-intercept scaled. Horizontal: y-intercept unchanged, x-intercepts scaled.

Order with shifts?▼

Apply stretches first, then shifts. For vertical: a*f(x)+c (stretch then shift).

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