Question

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.

f(x) = 5x + 4x^2

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

Answer 1

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.