4. Polynomial Functions

Understanding Polynomial Functions

4. Polynomial Functions

Understanding Polynomial Functions

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Multiple Choice

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\left(x\right)=2+x$

Polynomial with $n=1,a_{n}=2$

Polynomial with $n=0,a_{n}=1$

Polynomial with $n=1,a_{n}=1$

Not a polynomial function.

Verified step by step guidance

First, understand what a polynomial function is. A polynomial function is an expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Examine the given function: $ f(x) = 2 + x $. This function is a sum of terms where each term is either a constant or a variable raised to a non-negative integer power.

Identify the terms in the function: $ 2 $ and $ x $. The term $ x $ is equivalent to $ x^1 $, which is a valid polynomial term.

Write the function in standard form. A polynomial is in standard form when its terms are ordered from highest degree to lowest degree. In this case, $ f(x) = x + 2 $ is already in standard form.

Determine the degree and leading coefficient of the polynomial. The degree is the highest power of the variable, which is 1 in this case. The leading coefficient is the coefficient of the term with the highest degree, which is 1 for the term $ x $.