Question

1. Write an equation for a polynomial with the following properties: it has even degree, it has at least 2 terms, and, as the inputs getlarger and larger in either the negative or positive directions, the outputs get larger and larger in the negative direction.

Answer 1

the polynomial must be even, so we chose x²

it has at least 2 terms, then we add 1 to the previous item, we get: x² + 1

to get outputs larger and larger in the negative direction, we have to multiply the previous item by -1 to get: -x² - 1

This function has a graph like the next one:

Then, -x² - 1 satisfies all the features needed