How do I do this? If someone could at least show me how to do one of them with full solutions, it would help me understand them all.
Any help would be greatly appreciated!
Thanks in advance!
Well, what do you KNOW about functions? Can I presume that you know how to factor?
Function (1), obviously has zeros at x= 0, 2, and -2 and only at those points. Only graphs A and D have that property. For x> 2, all factors, x, x-2, and x+2, are positive so, because of the "-" in front, the f(x)< 0 for x> 2 and only D has that property.
Function (2), has zeros at x= 0, x= 2, x= -2, x= 1, and x= -1. C is the only graph that has that property.
Function (3), has zeros only at x= 0 and x= 2 (and a double root at x= 0 so the graph is tangent to the x-axis at x= 0). B is the only graph having that property.
Function (4), has zeros at x= 0, x= 2, and x= -2 and, as with (1), A and D have that property. But now, for x> 2, f(x)> 0 and only A has that property.