Question

Is the following a power function, a polynomial, both, or neither?

f(x)=4x³+4x²+5x+3
Select the correct answer below:
a Power function
b Polynomial function
c Both Power and Polynomial
d Neither Power nor Polynomial

Answer 1

The given function is a polynomial due to its form with non-negative integer powers of x; it is not a power function as it has more than one term, so it is a polynomial function. Option number b is correct.

Step-by-step explanation:

The given function f(x) = 4x³ + 4x² + 5x + 3 is a polynomial function because it is composed of terms that are non-negative integer powers of x, added or subtracted together. However, it is not a power function.

A power function is of the form f(x) = kxn, where 'k' is a constant and 'n' is a real number, and it contains exactly one term. Therefore, given the definition of both types of functions, the correct answer to whether the function is a power function, a polynomial, both, or neither is b) Polynomial function.