Special functions

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Absolute value or mod function

The absolute value (or modulus) |x| of a real number x is the non-negative value of x without regard to its sign. Namely, |x| = x for a positive x, |x| = − x for a negative x, and |0| = 0. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero.


Graph of absolute value of x


Exponential function

In mathematics, the exponential function is the function ex, where e is the number (approximately 2.718281828) such that the function ex, is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change (i.e. percentage increase or decrease) in the dependent variable. The function is often written as exp(x).


Graph of the exponential function ex


Trigonometric functions


A right angled triangle


Sine function


Cosine function


Tangent function


Graphs of Sin(x), Cos(x) and Tan(x)


Relation between Trigonometric functions