Range Calculator

Estimate the range of f(x) by evaluating it across its domain and reporting observed min/max.

About Range Calculator

This calculator estimates the range (set of output values) of f(x) by evaluating it at 5001 sample points across the specified domain. It reports the observed minimum and maximum values and where they occur. Note: the true range may extend beyond these bounds if the function is unbounded.

Formula

Range estimation

Range ≈ [min f(x), max f(x)] for x in [lo, hi]

lo: Domain lower bound
hi: Domain upper bound

Worked example

With the default values below, Range Calculator returns Estimated Range of [-0.7946, 10.544]. Change any input above and every figure here is recalculated in your browser.

Inputs used

f(x): sin(x) + x^2/10
Domain lower bound: -10
Domain upper bound: 10

Results

Estimated Range: [-0.7946, 10.544]
Minimum f(x): -0.794581
Maximum f(x): 10.544021
Min occurs at x ≈: -1.3080
Max occurs at x ≈: -10.0000

Step by step

1Values used
2Range estimation
3Estimated Range= [-0.7946, 10.544]
4Minimum f(x)= -0.794581
5Maximum f(x)= 10.544021
6Min occurs at x ≈= -1.3080
7Max occurs at x ≈= -10.0000

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Is this exact?

No — it is a numerical estimate. Extreme values between sample points may be missed, and truly unbounded functions cannot be fully characterized.

What if the function has vertical asymptotes?

Points where the function is undefined are skipped. The range only reflects finite output values found during sampling.