Whether the given function is a polynomial function. k(x) = –3x6 – 0.7x + x3

Yes, it is.

Step-by-step explanation:

A polynomial is one term or a sum of terms. A term is a single number or a number multiplied by one of more variables.

-3x^6 is a term since it is made up of a number, -3, called a coefficient, and many variables. The x is to the 6th power, so there are 6 factors of x.

-0.7x is also a term since it is made up of a coefficient, -0.7, and one variable, the x.

Finally, x^3 is also a term since it is the coefficient 1 multiplied by x^3.

Since the right side of the function is the sum of terms, it is a polynomial. The function is thus a polynomial equation.

The degree of a term is the sum of the exponents of all the variables of the term. Remember that a variable by itself is the same as the variable raised to the 1st power and has degree 1.  The degree of a polynomial is the same as the degree of the term with highest degree.

-3x^6 has degree 6

-0.7x has degree 1

x^3 has degree 3

Since the highest degree of all terms is 6, the entire polynomial is of of degree 6.