Which one of the following equations could possibly have the graph given below?
\(y = (3-x)^2(3+x)^2(1-x)\);
\(y = -x^2(x-9)(x^2-3)\);
\(y = (x-6)(x-2)^2(x+2)^2\);
\(y = (x^2-1)^2(3-x)\).
If the curve touches the \(x\)-axis at \(x=a\), what do we know about the equation of the curve?
What happens as \(x\) approaches \(\pm \infty\) for each of these equations?