Sketch the graph y=-x^3, using this sketch y=-x^(1/3)
The first step in figuring out this question is to first determine what the y=x3 looks like.If you are not already fimilar with this function, you can use some basic principles to find out what it looks like.When x=0 we know y=0 so we know this graph crosses the origin at 0, using this information you can determine that there are 3 roots at 0 because it is (x-0)3 = x3.You also know it goes up quickly and down quickly by determining a few points such as:x=-2 ---> y=-8x=-1 ---> y=-1x=0 ---> y=0x=1 ---> y=1x=2 ---> y=8One you have determined what y=x3 looks like you use graph transformations knowledge to determine the rest.Say y=f(x) then what is y=-f(x)?It is just a reflection in the x axis.The second part of the question requires you to understand that 1/x3 = x1/3 so the two graphs are just each others reciprocals. A reciprocal just means it is a reflection in the line y=x.
