**Monomial functions** are expressions which contain only one term.

Any number by itself is a monomial:

- 67,
- 8,900,
- 230,000

If you multiply variables (e.g. x, y, or z) along with the numbers, those are also monomials. For example:

- 2x,
- 3x
^{2}, - 45xyz,
- 905abc,
- 75xz
^{2}.

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).

Monomial functions can be:

- Any monomial. For example, y = 3.
- Any monomial, multiplied by another monomial. For example, y = 2 * 5 = 10
- Any monomial multiplied by a constant. For example y = 2 * 2x = 4x.

### What isn’t a monomial?

Something that often makes things clearer is seeing what *isn’t* a monomial function:

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

All of these above 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.

For example: 4 * a * b^{2} * c^{2}.

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.

This number is sometimes referred to as *order *when it comes to solving series.

**CITE THIS AS:**

**Stephanie Glen**. "Monomial Function" From

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