## What is a Monomial Function?

A**monomial function**is an expression with only one term. The power function f(x) = ax

^{n}is sometimes called “the” monomial function [1], but there are other possibilities. For example, a polynomial function is the sum of many monomial functions; If there’s only one term in a polynomial function, then it is a monomial function [2].

Monomial functions can take many forms:

**A monomial**(a number by itself is a “monomial”). These single-valued functions are usually called constant functions:- y = 67,
- y = π
- y = 230,000

**A monomial, multiplied by another monomial.**For example, y = 2 * 5 = 10**A monomial multiplied by a constant/variable combination.**For example y = 2 * 2x = 4x. If you multiply any variables (e.g. x, y, or z) along with the numbers, those are also monomials. For example:- 2x,
- 3x
^{2}, - 45xyz,
- 905abc,
- 75xz
^{2}.

## What isn’t a monomial?

A variable with a **negative exponent** is the same as having that variable in the denominator. Therefore, if you have an function that has an expression with a negative exponent,* it isn’t a monomial* (it’s a polynomial function).

Other examples of what *isn’t* a monomial function:

- 4x + 2
- 70a
^{2 }+ 30b – 7c^{3} - 45y
^{6 }– 42z^{4 }– 3y + 4z – 1 - 10x
^{-2}

All of the above expressions are not monomial functions since they have either addition or subtraction. Or, as in the last case, there’s a negative exponent. If the exponent were changed to be positive, meaning it would look like this, 10x^{2}, then it will be a monomial.

The** addition or subtraction of two or more monomials isn’t a monomial**. But if you separate their parts, you’ll get monomials. For example, the first one (4x + 2) is made of two parts, 4x and 2. Both of these by themselves will be monomials.

### Degrees of monomial function

To calculate the degree of a monomial function, sum the exponents of each variable.

**Example**: What is the degree of 4 * a * b^{2} * c^{2}?

**Solution**: The degree of the constant 4 is zero (i.e. there’s no exponent). However, the degrees of the variables are:

- a = 1
- b = 2
- c = 2

So, 1 + 2 + 2 = 5.

The *degree* is sometimes called the *order *when it comes to solving series.

## References

[1] Real Functions. Retrieved July 13, 2021 from: https://www.et.byu.edu/~vps/ET502WWW/TABLES-PDF/F.pdf

[2] Main Ideas. Retrieved July 13, 2021 from: https://ximera.osu.edu/fall18calcvids/o/basicderivrules/basicderivrules/preO

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