Utilize our Domain and Range Calculator to quickly identify valid input values and possible output values for various mathematical functions. Understand key concepts like restrictions for denominators, square roots, and logarithms effortlessly. This tool helps visualize where your functions are defined and what values they can produce for specific function types.
Formula:
Finding the domain and range involves identifying specific rules for different function types:
- Polynomial Functions (e.g., f(x) = ax2 + bx + c): No intrinsic restrictions. Domain: All Real Numbers ((-∞, ∞)).
- Rational Functions (e.g., f(x) = 1/(x-k)): The denominator cannot be zero. So,
x - k ≠ 0. - Square Root Functions (e.g., f(x) = √(x-k)): The expression under the radical must be non-negative. So,
x - k ≥ 0. - Logarithmic Functions (e.g., f(x) = log(x-k)): The argument must be positive. So,
x - k > 0.
This calculator focuses on these common restrictions, where 'k' represents a constant shift or critical value in simplified function forms.