Based ONLY on the maximum number of turning points, which of the following graphs could NOT be the graph of the given function? f ( x ) = x 3 + 1 f\left(x\right)=x^3+1 f ( x ) = x 3 + 1

In this problem based only on the number of maximum turning points of our function, we want to determine which of the following graphs could not be the graph of our given function, which is f of x is equal to x cubed plus 1. So we might actually know what the shape of this graph should look like but here we are only basing it on the turning points. So let's go ahead and look at our turning points here. Now remember the maximum number of turning points is simply n minus 1 where n is our degree. In this case, our degree is 3. So 3 minus 1 gives us 2, our maximum number of turning points. So it can only have 2 turning points at an absolute max. So let's go ahead and take a look at our graphs down here. Now, in graph a, looking for my turning points, I have two points where my graph changes direction. Now this does not go beyond my maximum of 2, so it actually could be this graph. Now looking at my second graph, graph b, this actually doesn't have any turning points. So it could be this graph as well. Now looking finally at graph c here and looking for all of my turning points, there are actually 1, 2, 3 points that this changes direction, which goes beyond my maximum of 2. So this absolutely cannot be the graph of my function. And so our answer here is c. Thanks for watching. That's all for this one.

Based ONLY on the maximum number of turning points, which of the ...

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Based ONLY on the maximum number of turning points, which of the following graphs could NOT be the graph of the given function? ﻿f(x)=x3+1f\left(x\right)=x^3+1f(x)=x3+1﻿

Based ONLY on the maximum number of turning points, which of the following graphs could NOT be the graph of the given function? $f\left(x\right)=x^3+1$