0. Functions

Common Functions

0. Functions

Common 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

Step 1: Understand the definition of a polynomial function. A polynomial function is an expression of the form f(x) = a_n * x^n + a_(n-1) * x^(n-1) + ... + a_1 * x + a_0, where n is a non-negative integer, and the coefficients a_n, a_(n-1), ..., a_0 are real numbers.

Step 2: Analyze the given function f(x) = 2 + x. This function consists of two terms: a constant term (2) and a linear term (x).

Step 3: Rewrite the function in standard form. Standard form arranges the terms in descending order of the powers of x. For f(x) = 2 + x, the standard form is f(x) = x + 2.

Step 4: Identify the degree of the polynomial. The degree of a polynomial is the highest power of x with a non-zero coefficient. In this case, the highest power of x is 1, so the degree is n = 1.

Step 5: Determine the leading coefficient. The leading coefficient is the coefficient of the term with the highest power of x. Here, the coefficient of x is 1, so the leading coefficient is a_n = 1.