
So, we still have x squared and x cubed functions graphed over here on this

coordinate plane. And here, I have y equals x to the 4th graphed as well. I'd

like you to take a second and compare the overall behavior of x to the 4th to x

squared. I know that all three of these graphs actually go through the origin.

Which makes sense, because zero taken to any power is just equal to zero. So we

plug in zero for x, and any of them, the y value is going to be zero as well.

However, both of the graphs that have even powers have that property that I

talked about in the previous answer video. Either end of the graph is going to

point in the same direction. Either going to have a sort of Ushape overall or

sort of upside down Ushape. The U for x to the 4th just happens to be a bit

steeper than it does for x squared. So, let's see if this pattern continues as

we move even higher in degree with our polynomial functions. Yet again, I've

added more graphs. One of these is the graph of y equals x to the 5th, and one

of them is the graph of y equals x to the 6th. So, thinking about the patterns

that you noticed over here with our first three graphs that you're considering,

what do you think the overall behavior of this 5th degree function will look

like versus the 6th degree function?