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- 1.2 Classes of Functions

Kenneth P.

Power Function

A function f given by the rule f(x) = x^{a}, where a is a fixed real number.

Polynomial Function

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Reciprocal Function

The special case of the function, f(x) = 1/x.

Root Function

A power function where a is a fraction, f is given by the rule f(x) = x^{a} = x^{1/n} = ^{n}√a.

Degree

The largest exponent present in a polynomial function.

Coefficient

The real numbers that multiply the power functions in a polynomial.

Constant Function

A polynomial function with a degree of zero.

Linear Function

A polynomial function with a degree of one.

Quadratic Function

A polynomial function with a degree of two.

Cubic Function

A polynomial function with a degree of three.

Rational Function

The ratio of two polynomial functions.

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Trigonometric Function

Functions including sin, cos, tan, cot, sec, or csc.

Periodicity

The tendency of a function to repeat itself in a regular pattern at established intervals.

Periodic Function

A function which has a period T > 0 if f(x) = f(x + T) for all x and T is the smallest positive real number with this property.

Algebraic Function

A function that contains only addition, subtraction, multiplication, division, and taking roots.

Transcendental Function

A function that is not algebraic. This includes trigonometric functions

and their inverses, exponential functions and their inverses.

Logarithmic Function

The inverse of an exponential function.

Absolute Value Funciton

A function which takes a part and makes it positive. It has more than one range.

Exponential Function

A function that contains a variable as an exponent, such as f(x) = 2^{x}.

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