Question

polynomial function has the form f(x)=axʲ bxᵏ where a and b are non zero constants, j and k are nonnegative integers. which of the following conditions guarantees that p is an even function?

Answer 1

A polynomial function is even if all the exponents of its variables are even numbers, ensuring the function's symmetry about the y-axis and that f(x) equals f(-x) for all x.

Step-by-step explanation:

To determine the conditions that guarantee a polynomial function f(x) = axj + bxk is an even function, we need to consider the powers j and k. An even function is symmetric about the y-axis, meaning that f(x) = f(-x) for all x in the domain of f.

Since even functions produce even functions when multiplied together and odd functions produce an even function when an odd number is multiplied by itself, both j and k must be even numbers. This ensures that each individual term axj and bxk is an even function, and their sum is also even.

Satisfying the condition f(x) = f(-x). Recall that in the context of polynomials, the solution of quadratic equations involves functions where the highest exponent is 2, which is an even number. For higher-degree polynomials to be even functions, all terms must have even powers.