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5 3.1 Graphs of Polynomials 183 In order to solve Example 3.1.3, we made good use of the graph of the polynomial y = V (x). So we
ought to turn our attention to graphs of polynomials in general. Below are the graphs of y = x2 ,
y = x4 , and y = x6 , side-by-side. We have omitted the axes so we can see that as the exponent
increases, the ‘bottom’ becomes ‘ﬂatter’ and the ‘sides’ become ‘steeper.’ If you take the the time
to graph these functions by hand,7 you will see why. y = x2 y = x4 y = x6 All of these functions are even, (Do you remember how to show this?) and it is exactly because
the exponent is even.8 One of the most important features of these functions which we can be
seen graphically is their end behavior. The end behavior of a function is a way to describe what
is happening to the function values as the x values approach the ‘ends’ of the x-axis:9 that is,
as they become small without bound10 (written x → −∞) and, on the ﬂip side, as they become
large without boun...
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