Describe the graph of the function at its roots. f (x) = (x - 2) 3 (x + 6) 2 (x + 12) At x = 2, the graph crossesdoes not intersecttouches the x-axis. At x = - 6, the graph crossesdoes not intersecttouches the x-axis. At x = - 12, the graph crossesdoes not intersecttouches the x-axis.

This type of problem can be decided by looking at whether the function is positive or negative in the vicinity of the zeros. There are three roots: - 12, - 6, and 2 at which the function is clearly 0. Look at the four intervals the x axis:

interval x<-12: function is negative (just test using a number <-12, say, - 13)

interval (-12,-6) : function is positive

interval (-6, 2) : function is negative

interval x>2: positive

From the above you deduce that at the roots the function must be crossing the x-axis (as opposed to just touching it) because the function value changes its sign every time.

Answer:the first option is crosses then touches lastly crosses again