Question: "Determine which functions are polynomial functions. For those..."

zachutnat4o

Answered question

2021-11-30

Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not.

h (x) = 3 - \frac{1}{2} x

Answer & Explanation

Heack1991

Beginner2021-12-01Added 13 answers

Step1
The polynomial expression consists of variables and their coefficients. The variables are presented in the
expression with exponents. The general form of polynomial equation of degree n is

P (x) = a_{n} x^{n} + a π ”^{'} + a_{n - 1} x^{n - 1} + \dots + a_{2} x^{2} + a_{1} x + a_{0}

.
The degree of a polynomial is the highest power of variable in the polynomial equation. A function is called a polynomial function if it can be expressed in the form of a polynomial expression. The solution of a polynomial
is the value for the variable ( x) that satisfies the polynomial equation.
Step2
Consider the equation

h (x) = 3 - \frac{1}{2} x

.
A polynomial function involves only positive integer powers forts variable. Here, in

h (x) = 3 - \frac{1}{2} x

, the variable is x and its power is non negative ( power equal to 1).
Hence, the given equation

h (x) = 3 - \frac{1}{2} x

is a polynomial function, which is of the form of a polynomial with degree one as

P (x) = a_{1} x = a_{0} .

The degree of a polynomial equation is the highest variable power of the polynomial.
Here, we have the highest power of polynomial

h (x) = 3 - \frac{1}{2} x i s 1

.
Hence, the function is a polynomial function with degree 1.

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