Question

Wich of the following functions is a polynomial?

a. f(x)=x
b. g(x)=log2x
c. r(x)=2x
d. s(x)=|x+2|

Answer 1

A polynomial function can be expressed as a sum of non-negative integer powers of x with real number coefficients. Given the options, f(x)=x and r(x)=2x are the functions that fit within this definition, making them polynomial functions.

Step-by-step explanation:

To determine which of the given functions is a polynomial, we must first understand the definition of a polynomial function. A polynomial function is one that can be expressed in the form f(x) = anxn + an-1xn-1 + ... + a2x2 + a1x1 + a0, where n is a non-negative integer, and the coefficients an, an-1, ..., a1, a0 are real numbers.

Looking at our options:

• f(x) = x can be written as f(x) = 1x1 + 0, which fits the form of a polynomial function.
• g(x) = log2x is not a polynomial function, as it contains a logarithm.
• r(x) = 2x can also be expressed in polynomial form as r(x) = 2x1 + 0.
• s(x) = |x+2| is not a polynomial since the absolute value function is not allowed in polynomial expressions.

Therefore, both f(x) and r(x) are polynomial functions.