3. Give a symbolic example of a quartic function that is even and \( f(x) \rightarrow-\infty \) as \( x \rightarrow \pm \infty \).

A great example of an even quartic function that meets your criteria is \( f(x) = -x^4 + 2x^2 \). This function is even because all the exponents of \( x \) are even, meaning \( f(x) = f(-x) \). As \( x \) approaches \( \pm \infty \), the \( -x^4 \) term dominates, causing \( f(x) \) to trend toward \( -\infty \). Essentially, it looks like a downward-opening "bowl" that dips lower and lower as you move away from the center! To visualize how this function behaves, sketch a graph! You’ll see it has a maximum point at the origin (0, 0) and approaches the negative infinity as \( x \) goes far to the left or right. The curve showcases the unique features of quartic functions while remaining even and trending toward negative infinity outside its central high point.