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. Identify the given function: \( f(x) = 2 + x \).
2. Determine if the function is a polynomial: 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.
3. Check the terms of the function: The function \( f(x) = 2 + x \) consists of two terms, \( 2 \) and \( x \). Both terms fit the criteria for a polynomial since \( 2 \) is a constant (which is a polynomial of degree 0) and \( x \) is a variable raised to the power of 1.
4. Write the function in standard form: A polynomial is in standard form when its terms are written in descending order of their degrees. The function \( f(x) = 2 + x \) can be rewritten as \( f(x) = x + 2 \).
5. Determine the degree and leading coefficient: The degree of a polynomial is the highest power of the variable in the polynomial. Here, the degree is 1 (from the term \( x \)), and the leading coefficient is the coefficient of the term with the highest degree, which is 1.