Below is a list of functions, then some graphs of these functions
functions- constant function: \( f(x) = c \), where \( c \) is a constant.
- identity function: \( f(x) = x \).
- polynomial functions: \( f(x) = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0 \), where \( a_i \) are constants and \( n \) is a non-negative integer.
- exponential function: \( f(x) = e^x \).
- logarithmic function: \( f(x) = \log_a(x) \), where \( a \) is a positive constant and \( x \) is the argument.
- trigonometric functions:
- sine function: \( f(x) = \sin(x) \).
- cosine function: \( f(x) = \cos(x) \).
- tangent function: \( f(x) = \tan(x) \).
- cosecant function: \( f(x) = \csc(x) \).
- secant function: \( f(x) = \sec(x) \).
- cotangent function: \( f(x) = \cot(x) \).
- inverse trigonometric functions:
- arcsine function: \( f(x) = \arcsin(x) \).
- arccosine function: \( f(x) = \arccos(x) \).
- arctangent function: \( f(x) = \arctan(x) \).
- arccosecant function: \( f(x) = \text{arccsc}(x) \).
- arcsecant function: \( f(x) = \text{arcsec}(x) \).
- arccotangent function: \( f(x) = \text{arccot}(x) \).
- hyperbolic functions:
- hyperbolic sine function: \( f(x) = \sinh(x) \).
- hyperbolic cosine function: \( f(x) = \cosh(x) \).
- hyperbolic tangent function: \( f(x) = \tanh(x) \).
- hyperbolic cosecant function: \( f(x) = \text{csch}(x) \).
- hyperbolic secant function: \( f(x) = \text{sech}(x) \).
- hyperbolic cotangent function: \( f(x) = \coth(x) \).
- inverse hyperbolic functions:
- inverse hyperbolic sine function: \( f(x) = \text{arcsinh}(x) \).
- inverse hyperbolic cosine function: \( f(x) = \text{arccosh}(x) \).
- inverse hyperbolic tangent function: \( f(x) = \text{arctanh}(x) \).
- inverse hyperbolic cosecant function: \( f(x) = \text{arccsch}(x) \).
- inverse hyperbolic secant function: \( f(x) = \text{arcsech}(x) \).
- inverse hyperbolic cotangent function: \( f(x) = \text{arccoth}(x) \).
plots
This began as an attempt to explain "functions" to my dad and my brother. It did not get far, but it is something. Enjoy?
identity \(y=x\)
square \(y=x^2\)
cube \(y=x^3\)
square root \(y=\sqrt{x}\)
cube root \(y=\sqrt{3}{x}\)
exponent \(y=e^x\)
natural log \(y=\ln (x) \)
rational \(y= \frac{1}{x} \)
sine \(y= \sin{x} \)
cosine \(y= \cos{x} \)
absolute value \(y= \operatorname{abs}{x} \)
floor \(y= \operatorname{floor}{x} \)
tranformations
In the scroll menu below, use the equation and sliders to investigate each of the functions. Change the letter of the function notation to see each function's transformations. For example delete the f and replace with a g to change the parent from a linear to a quadratic.