# Table of Domain and Range of Common Functions

A table of domain and range of common and useful functions is presented.
Also a Step by Step Calculator to Find Domain of a Function and a Step by Step Calculator to Find Range of a Function are included in this website.

## Algebraic Functions

FunctionDomainRange
$$f(x) = x$$$$(-\infty, +\infty)$$$$(-\infty, +\infty)$$
$$f(x) = x^2$$$$(-\infty, +\infty)$$$$[0, +\infty)$$
$$f(x) = x^3$$$$(-\infty, +\infty)$$$$(-\infty, +\infty)$$
$$f(x) = x^n$$, $$n$$ even$$(-\infty, +\infty)$$$$[0, +\infty)$$
$$f(x) = x^n$$, $$n$$ odd$$(-\infty, +\infty)$$$$(-\infty, +\infty)$$
$$f(x) = |x|$$$$(-\infty, +\infty)$$$$[0, +\infty)$$
$$f(x) = \sqrt{x}$$$$[0, +\infty)$$$$[0, +\infty)$$
$$f(x) = \sqrt[3]{x}$$$$(-\infty, +\infty)$$$$(-\infty, +\infty)$$

## Trigonometric Functions

FunctionDomainRange
$$f(x) = \sin(x)$$$$(-\infty, +\infty)$$$$[-1, 1]$$
$$f(x) = \cos(x)$$$$(-\infty, +\infty)$$$$[-1, 1]$$
$$f(x) = \tan(x)$$All real numbers except $$\frac{\pi}{2} + n\pi$$$$(-\infty, +\infty)$$
$$f(x) = \sec(x)$$All real numbers except $$\frac{\pi}{2} + n\pi$$$$(-\infty, -1] \cup [1, +\infty)$$
$$f(x) = \csc(x)$$All real numbers except $$n\pi$$$$(-\infty, -1] \cup [1, +\infty)$$
$$f(x) = \cot(x)$$All real numbers except $$n\pi$$$$(-\infty, +\infty)$$

## Inverse Trigonometric Functions

FunctionDomainRange
$$f(x) = \sin^{-1}(x)$$$$[-1, 1]$$$$[-\frac{\pi}{2}, \frac{\pi}{2}]$$
$$f(x) = \cos^{-1}(x)$$$$[-1, 1]$$$$[0, \pi]$$
$$f(x) = \tan^{-1}(x)$$$$(-\infty, +\infty)$$$$(-\frac{\pi}{2}, \frac{\pi}{2})$$
$$f(x) = \sec^{-1}(x)$$$$(-\infty, -1] \cup [1, +\infty)$$$$[0, \frac{\pi}{2}) \cup [\pi, \frac{3\pi}{2})$$
$$f(x) = \csc^{-1}(x)$$$$(-\infty, -1] \cup [1, +\infty)$$$$(-\pi, -\frac{\pi}{2}] \cup (0, \frac{\pi}{2}]$$
$$f(x) = \cot^{-1}(x)$$$$(-\infty, +\infty)$$$$(0, \pi)$$

## Logarithmic and Exponential Functions

FunctionDomainRange
$$f(x) = a^x$$$$(-\infty, +\infty)$$$$(0, +\infty)$$
$$f(x) = \log_a(x)$$$$(0, +\infty)$$$$(-\infty, +\infty)$$
$$f(x) = a^x + k$$, $$k$$ constant$$(-\infty, +\infty)$$$$(k, +\infty)$$
$$f(x) = \log_a(x - k)$$, $$k$$ constant$$(k, +\infty)$$$$(-\infty, +\infty)$$

## Hyperbolic Functions

FunctionDomainRange
$$\sinh(x) = \frac{e^x - e^{-x}}{2}$$$$(-\infty, +\infty)$$$$(-\infty, +\infty)$$
$$\cosh(x) = \frac{e^x + e^{-x}}{2}$$$$(-\infty, +\infty)$$$$[1, +\infty)$$
$$\tanh(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}}$$$$(-\infty, +\infty)$$$$(-1, 1)$$
$$\coth(x) = \frac{e^x + e^{-x}}{e^x - e^{-x}}$$$$(-\infty, 0) \cup (0, +\infty)$$$$(-\infty, -1) \cup (1, +\infty)$$
$$\operatorname{sech}(x) = \frac{2}{e^x + e^{-x}}$$$$(-\infty, +\infty)$$$$(0, 1)$$
$$\operatorname{csch}(x) = \frac{2}{e^x - e^{-x}}$$$$(-\infty, 0) \cup (0, +\infty)$$$$(-\infty, 0) \cup (0, +\infty)$$