Domain and Range Calculator
Find the domain and range for common function families such as linear, quadratic, square-root, reciprocal, logarithmic, and exponential functions.
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What this calculator teaches
Domain means all input x-values that are allowed. Range means all output y-values the function can produce.
This calculator focuses on the common parent functions students meet in Algebra 2 and Precalculus. It shows how shifts and coefficients change restrictions.
Formula & Symbols
| Concept | Formula | Meaning |
|---|---|---|
| Domain | x values allowed | Inputs that do not break the function. |
| Range | y values possible | Outputs produced by the function. |
| Quadratic vertex | y=a(x-h)^2+k | The vertex is (h,k), so range depends on whether a is positive or negative. |
Step-by-Step Examples
- For y = √(x - 3) + 2, the expression under the radical must be nonnegative.
- x - 3 ≥ 0, so x ≥ 3.
- The smallest output is 2.
- For y = 1/(x - 4) + 2, the denominator cannot be zero.
- x - 4 ≠ 0, so x ≠ 4.
- The horizontal asymptote is y = 2, so y ≠ 2.
Where students use this
Common Mistakes to Avoid
Domain is about x-values. Range is about y-values.
A denominator cannot equal zero, so reciprocal functions exclude one x-value.
For quadratics, the range starts or ends at the vertex y-value k.
Frequently Asked Questions
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Formula Explorer connections
Interpretation: This formula describes an algebraic relationship among variables, functions, equations, roots or sequences. Assumption: Respect the expression’s domain and excluded values. Check roots in the original equation because transformations can introduce extraneous solutions.