Final answer:
The degree of the polynomial f(x) = 4x - 8x⁴ is 4, as -8x⁴ is the term with the highest power of x.
Step-by-step explanation:
The degree of the polynomial f(x) = 4x – 8x⁴ is determined by the highest power of the variable x in the polynomial expression. In this case, the term with the highest power of x is -8x⁴, which means the polynomial is of the fourth degree. The degree of a polynomial is indicative of its most dominant term when x goes to extremely large numbers or extremely negative numbers and it also dictates the general shape of the graph of the polynomial.