# Rescale

Rescale[x,{min,max}]

gives x rescaled to run from 0 to 1 over the range min to max.

Rescale[x,{min,max},{ymin,ymax}]

gives x rescaled to run from ymin to ymax over the range min to max.

Rescale[list]

rescales each element of list to run from 0 to 1 over the range Min[list] to Max[list].

# Details • Rescale[x,{min,max}] is effectively equivalent to (x-min)/(max-min).
• For exact numeric quantities, Rescale internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable \$MaxExtraPrecision.
• Rescale works with complex numbers and symbolic quantities.

# Examples

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## Basic Examples(3)

Rescale to run from 0 to 1 over the range to 10:

Rescale so that all the list elements run from 0 to 1:

Plot over a subset of the reals:

## Scope(24)

### Numerical Evaluation(5)

Evaluate numerically:

Complex number inputs:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate efficiently at high precision:

Rescale threads over lists in its first argument:

Specify the maximum and minimum values:

### Specific Values(6)

Value at zero:

Values at the endpoints:

Rescale x to run from to when its values run from to :

Value with a degenerate third argument:

Rescale a list with symbolic quantities:

Find a value of x for which the Rescale[x,{-2,2}]=1:

### Visualization(3)

Visualize two Rescale expressions with reversed endpoints in the second argument:

Visualize two Rescale expressions with reversed endpoints in the third argument:

Visualize Rescale in the complex plane:

### Function Properties(4)

Rescale is defined for all real and complex inputs in its first argument:

The domain of the endpoints in the second and third arguments:

The only restriction is that endpoints in the second argument must be distinct:

Rescale achieves all real and complex values:

The one-argument form for a list can be expressed using Min and Max:

Rescale[list] is effectively Rescale[list,{Min[list],Max[list]}]:

### Differentiation and Integration(6)

First derivative with respect to x:

First and second derivatives with respect to x:

Formula for the  derivative with respect to x:

First derivative with respect to an endpoint:

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

Definite integral:

## Applications(1)

Make a Celsius-to-Fahrenheit conversion table:

## Properties & Relations(3)

In the complex plane, Rescale just scales and rotates a region:

Reversing both range specifications gives back the same result:

Rescale is effectively linear with respect to its first argument: