Range Calculator
Estimate the range of f(x) by evaluating it across its domain and reporting observed min/max.
Inputs
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
Values used
f(x) = sin(x) + x^2/10; Domain lower bound = -10; Domain upper bound = 10
Range estimation
Range ≈ [min f(x), max f(x)] for x in [lo, hi]
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
How it works
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
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.