What is domain?
The set of x-values for which the expression is defined in the reals.
Domain and Range Calculator
Select a function family and coefficients to read domain and range in interval language.
Select function family
Choose sqrt, reciprocal, log, or quadratic and enter the relevant constants.
About this calculator
How to use Domain and Range Calculator, plus the formulas and logic behind the results.
Tool description
Domain is the set of allowed inputs; range is the set of possible outputs. Restrictions come from even roots, division by zero, and logs.
How to use
- Pick the function family.
- Enter coefficients a, b, and c as needed.
- Select Calculate to view domain and range descriptions.
- Read notes about vertex or asymptotes when relevant.
Formulas & reference
√(ax+b): ax+b ≥ 01/(x−c): x ≠ c; y ≠ 0log(ax+b): ax+b > 0ax²+bx+c: domain ℝ; range depends on vertex and sign of a
Common restrictions
- Even root: inside ≥ 0
- Denominator ≠ 0
- Log argument > 0
- Quadratic always defined on ℝ
Calculation logic
Applies standard real-analysis restrictions for each family and describes intervals in text form.
Results are for real numbers. Complex values are not included.
Domain and Range Calculator FAQ
Common questions about this calculator and how to use the results.
What is range?
The set of y-values the function can actually output.
Why exclude y = 0 for 1/(x−c)?
A nonzero numerator over a linear denominator never hits zero.
How is quadratic range found?
From the vertex y-value and whether the parabola opens up or down.
Does log mean ln here?
This mode uses common log (base 10); the domain condition is the same for any base > 0, ≠ 1.
What if a = 0 in sqrt mode?
Then f is constant √b when b ≥ 0, or undefined if b < 0.