Which one of the following equations could possibly have the graph given below?

  1. \(y = (3-x)^2(3+x)^2(1-x)\);

  2. \(y = -x^2(x-9)(x^2-3)\);

  3. \(y = (x-6)(x-2)^2(x+2)^2\);

  4. \(y = (x^2-1)^2(3-x)\).

Graph that tends to minus infinity as x tends to infinity, and tends to infinity as x tends to minus infinity. It touches the x axis twice, once for a positive x value and once for a negative one, and finally crosses the x axis from above to below for an x value larger than these values. Its value at 0 is positive.

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?