Final answer:
The function f(x) = 5x + 4x^2 is a polynomial function of degree 2 because the highest power of x in the function is 2, as seen in the term 4x^2.
Step-by-step explanation:
The function f(x) = 5x + 4x^2 is a polynomial function because it is composed of terms that are non-negative integer powers of x. In this case, the function has a constant term (0x0), a linear term (5x1), and a quadratic term (4x2). The highest degree of the terms determines the degree of the polynomial. Since the highest power of x is 2, the function is of degree 2.
Answer choices for the given function f(x) = 5x + 4x^2 are:
- a) Polynomial function of degree 1
- b) Polynomial function of degree 2
- c) Not a polynomial function because it contains terms of different degrees
- d) Not a polynomial function because it is not continuous
Therefore, the correct answer is (b) Polynomial function of degree 2.