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Elementary functions are functions built from basic operations (e.g. addition, exponentials, logarithms...) Algebraic functions[edit] Algebraic functions are functions that can be expressed as the solution of a polynomial equation with integer coefficients. Polynomials: Can be generated by addition, multiplication, and exponentiation alone. Constant function: polynomial of degree zero, graph is a horizontal straight line Linear function: First degree polynomial, graph is a straight line. Quadratic function: Second degree polynomial, graph is a parabola. Cubic function: Third degree polynomial. Quartic function: Fourth degree polynomial. Quintic function: Fifth degree polynomial. Sextic function: Sixth degree polynomial. Rational functions: A ratio of two polynomials. Nth root Square root: Yields a number whose square is the given one x^{\frac{1}{2}} \!\ . Cube root: Yields a number whose cube is the given one x^{\frac{1}{3}} \!\ . Elementary transcendental functions[edit] Transcendental functions are functions that are not algebraic. Exponential function: raises a fixed number to a variable power. Hyperbolic functions: formally similar to the trigonometric functions. Logarithms: the inverses of exponential functions; useful to solve equations involving exponentials. Natural logarithm Common logarithm Binary logarithm Power functions: raise a variable number to a fixed power; also known as Allometric functions; note: if the power is a rational number it is not strictly a transcendental function. Periodic functions Trigonometric functions: sine, cosine, tangent, etc.; used in geometry and to describe periodic phenomena. See also Gudermannian function. Sawtooth wave Square wave Triangle wave |
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