Is y=-2 x 5^x a monomial function?
The names monomial, binomial, etc, are usually reserved for polynomial functions, where all the terms are just powers of x (or other variables).
The above function, with its 5^x factor is not a polynomial, as generally used.
The terms of a polynomial are separated by + and - signs.
To determine if the function y = -2x*5^x is a monomial function, we need to understand what a monomial function is.
A monomial function is a function that can be written as a single term, where the term consists of a constant multiplied by a variable raised to a non-negative integer exponent.
Looking at the given function y = -2x*5^x, we have two terms: -2x and 5^x.
The first term, -2x, consists of a constant (-2) multiplied by a variable (x) raised to the first power. This term can be written as -2x^1, which satisfies the definition of a monomial.
The second term, 5^x, consists of a constant (5) raised to the power of a variable (x). This term can be written as 5^x, which also satisfies the definition of a monomial.
Since each term in the function y = -2x*5^x can be expressed as a monomial, we can conclude that the given function is a monomial function.