Question

What is a monomial function?

Answer 1

Hint: Monomial functions are mathematical expressions that contain only one term and this term can be a constant, an integer, a variable or a product. They cannot be fractional or have a negative exponent.

Complete step-by-step solution:
Let us see what a monomial function is. Monomial functions are mathematical expressions that contain only one term. These terms can be a constant, an integer, a variable or a product. Any number (constants) can be a monomial. For example, let us consider a function $f\left( x \right)=6$ . This function is a monomial function since there is only one term.
Similarly, monomial functions can also have variables. For example, let us consider a function $f\left( x \right)=x$ and $f\left( y \right)=xyz$ . Both these functions are monomial since only one term is present.
For a monomial function, the degree of the function is not considered. For example, let us consider a function $f\left( x \right)={{x}^{2}}{{y}^{3}}$ . This function is monomial since only one term is present.
Now, let us consider a function $f\left( x \right)={{x}^{2}}+{{y}^{2}}-c-xy$ . This function is not a monomial function since there are 4 terms present in this function. Now consider a function $f\left( x \right)=-\dfrac{1}{2}$ . This function is not a monomial since this function has a fractional term.
Therefore, monomial functions are mathematical expressions that contain only one term and this term can be a constant, an integer, a variable or a product. They cannot be fractional or have a negative exponent.

Note: Students may confuse monomial function with binomial and trinomial functions. Binomial functions are the functions with two terms while trinomial functions are those with three terms. Binomial and trinomial can contain variable, coefficient, exponents and constant.