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

• A. Polynomial with $n=1,a_{n}=2$
• B. Polynomial with $n=0,a_{n}=1$
• C. Polynomial with $n=1,a_{n}=1$
• D. Not a polynomial function.

Answer: (C)

Verified step by step guidance

1. 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.
2. 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.
3. Identify the terms in the function: \( 2 \) and \( x \). The term \( x \) is equivalent to \( x^1 \), which is a valid polynomial term.
4. 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.
5. 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 \( x \).