Question

In problems 15–26, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, explain why not. 20. f(x) = x² - 12

Answer 1

The function f(x) = x² - 12 is a polynomial function, specifically a quadratic function due to the presence of the x² term. The degree of this polynomial is 2.

Step-by-step explanation:

The function given in Problem 20, f(x) = x² - 12, is indeed a polynomial function. A polynomial function is one that is composed of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The degree of a polynomial function is determined by the highest power of the variable in any of the terms. In this case, the function contains the term x², which indicates it's a second-order polynomial more commonly known as a quadratic function. The highest power of x in the function is 2, so the degree of the polynomial is also 2.