Determine whether the function is even, odd or neither. f(x)=5x^7-2x^3 Which term describes the function? A. even B. odd C. neither

To determine whether the function \( f(x) = 5x^7 - 2x^3 \) is even, odd, or neither, we need to check the following properties:<br /><br />1. A function \( f(x) \) is even if \( f(-x) = f(x) \) for all \( x \).<br />2. A function \( f(x) \) is odd if \( f(-x) = -f(x) \) for all \( x \).<br /><br />Let's apply these properties to the given function:<br /><br />First, calculate \( f(-x) \):<br />\[ f(-x) = 5(-x)^7 - 2(-x)^3 \]<br /><br />Simplify the expression:<br />\[ f(-x) = 5(-x^7) - 2(-x^3) \]<br />\[ f(-x) = -5x^7 + 2x^3 \]<br /><br />Now, compare \( f(-x) \) with \(-f(x)\):<br />\[ -f(x) = -(5x^7 - 2x^3) \]<br />\[ -f(x) = -5x^7 + 2x^3 \]<br /><br />We see that:<br />\[ f(-x) = -f(x) \]<br /><br />Since \( f(-x) = -f(x) \), the function \( f(x) = 5x^7 - 2x^3 \) is an odd function.<br /><br />Therefore, the correct answer is:<br />B. odd