Describe the end behavior of the function. \( f(x)=11-18 x^{2}-5 x^{3}-12 x^{4}-2 x \)

As \( x \) approaches positive or negative infinity, the leading term of the polynomial dominates the behavior of the function. Here, the leading term is \( -12x^4 \), which is a degree 4 polynomial with a negative coefficient. This means that both as \( x \to \infty \) and \( x \to -\infty \), \( f(x) \) will approach \( -\infty \). So, graphically, the ends of the function go downwards on both sides. When analyzing the end behavior mathematically, you can visualize the polynomial as a rollercoaster: it starts high and goes low as you venture towards the edges of the track. This characteristic of even-degree polynomials with negative leading coefficients makes them create a U-like shape that extends downwards in both directions!