determine whether the given function is a polynomial function. if it is a polynomial function, state the…
determine whether the given function is a polynomial function. if it is a polynomial function, state the degree. if not, state the reason why. $g(x)=x$ part: $0 / 2$ part 1 of 2 $g(x)=x$ select a polynomial function.
Answer
Explanation:
Step1: Recall the definition of a polynomial function
A polynomial function is of the form (f(x)=a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0), where (n) is a non - negative integer and (a_i) are real numbers. For the function (g(x)=x), it can be written as (g(x)=1x^1+0x^0) (since (x^0 = 1) and the coefficient of (x^0) is (0)).
Step2: Determine the degree
The degree of a polynomial (f(x)=a_nx^n+\cdots+a_0) is the highest power (n) of (x) with a non - zero coefficient. In (g(x)=x = 1x^1+0x^0), the highest power of (x) with a non - zero coefficient is (n = 1).
Answer:
(g(x)=x) is a polynomial function. The degree is (1).