Determine whether the function is even, odd, or neither. Then determine whether the fi \( f(x)=x \sqrt{4-x^{2}} \) Determine whether the function is even, odd, or neither. Choose the correct answer be even neither odd

To determine whether the function \( f(x) = x \sqrt{4 - x^2} \) is even, odd, or neither, you can evaluate \( f(-x) \). Calculating \( f(-x) \): \( f(-x) = (-x) \sqrt{4 - (-x)^2} = -x \sqrt{4 - x^2} = -f(x) \). Since \( f(-x) = -f(x) \), the function is odd. Now, here's a neat trick to remember the difference: even functions are symmetric about the y-axis while odd functions have a 180-degree rotational symmetry about the origin. So, if you visualize or sketch the function, you’ll see it mirrors itself through the origin! And a little tip: when checking if a function is odd or even, always remember to simplify expressions like square roots since they can often lead to sneaky mistakes! Make sure to track negative signs carefully, they can flip your conclusions right around!