H. Algebraic Function

What is an Algebraic Function?

An algebraic function is a function that involves only algebraic operations. These operations include addition, subtraction, multiplication, division, and exponentiation. Based on this definition, let us see some examples of algebraic functions and non-algebraic functions.

Algebraic Function Examples

Here are some examples of algebraic functions. Note that algebraic functions should include only the operations, +, -, ×, ÷, integer and rational exponents. These notations result in algebraic functions such as a polynomial function, cubic function, quadratic function, linear function, and is based on the degree of the equations involved.

· f(x) = x² - 5x + 7

· g(x) = √x

· h(x) = (3x + 1) / (2x - 1)

· k(x) = x³

Identifying Algebraic Functions

If a function includes only the above-mentioned operations (+, -, ×, ÷, exponents (also roots)), then we can say that it is an algebraic function. Let us have a look at non-algebraic functions as well to avoid confusion.

Non-Algebraic Function Examples

Non-algebraic functions include trigonometric functions, logarithmic functions, absolute value functions, exponential functions, etc. Here are some examples.

· f(x) = sin (3x + 2)

· g(x) = log x

· h(x) = 3^x