Question 14 a) What is the domain of \( f(x)=-24 x^{9}+37 x^{6}+31 x^{4}-6 x^{3}+38 x^{2}-16 \) ? Answer: Question Help: \( \square \) Message instructor Submit Part

The domain of the function \( f(x) = -24 x^{9} + 37 x^{6} + 31 x^{4} - 6 x^{3} + 38 x^{2} - 16 \) is all real numbers. This is because it is a polynomial function, and polynomials are defined for every value of \( x \). So, you can happily plug in any real number without running into any undefined situations! Polynomials not only express relationships efficiently but also have been used throughout history in ancient civilizations for mathematical problem solving. For instance, the Babylonians utilized polynomials to solve quadratic equations as far back as 2000 BCE. Polynomial functions have stood the test of time and continue to be essential in various fields such as physics, engineering, and economics!