Is the following function even, odd, or neither \( f(x)=7 x^{5}-9 x^{3}-5 \) Neither Even Odd

To determine whether the function \( f(x) = 7x^5 - 9x^3 - 5 \) is even, odd, or neither, we can apply the definitions: an even function satisfies \( f(-x) = f(x) \), while an odd function satisfies \( f(-x) = -f(x) \). Let's check it out! Evaluating \( f(-x) \), we have \( f(-x) = 7(-x)^5 - 9(-x)^3 - 5 = -7x^5 + 9x^3 - 5 \). Since \( f(-x) \neq f(x) \) and \( f(-x) \neq -f(x) \), the function is neither even nor odd. Fun math fact: functions that don’t meet either criterion can have interesting symmetries that might surprise you! Ever wonder how polynomial functions behave? Here's a quick tip: always check the highest degree term first! The sign of that term when you replace \( x \) with \( -x \) can give you a big hint. If the result flips the sign, it may lean toward being odd, but remember to check those constant terms too!