Calculus How To

Monomial Function

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Calculus Definitions >

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,
  • 3x2,
  • 45xyz,
  • 905abc,
  • 75xz2.

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:

  1. Any monomial. For example, y = 3.
  2. Any monomial, multiplied by another monomial. For example, y = 2 * 5 = 10
  3. 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+ 30b – 7c3
  • 45y– 42z– 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, 10x2, 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 * b2 * c2.
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.

Stephanie Glen. "Monomial Function" From Calculus for the rest of us!

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