Stitz-Zeager_College_Algebra_e-book

7 we now revisit the data set from exercise 4b in

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Unformatted text preview: .8. 8 184 Polynomial Functions End Behavior of functions f (x) = axn , n even. Suppose f (x) = axn where a = 0 is a real number and n is an even natural number. The end behavior of the graph of y = f (x) matches one of the following: a>0 a<0 We now turn our attention to functions of the form f (x) = xn where n ≥ 3 is an odd natural number.13 Below we have graphed y = x3 , y = x5 , and y = x7 . The ‘flattening’ and ‘steepening’ that we saw with the even powers presents itself here as well, and, it should come as no surprise that all of these functions are odd.14 The end behavior of these functions is all the same, with f (x) → −∞ as x → −∞ and f (x) → ∞ as x → ∞. y = x5 y = x3 y = x7 As with the even degreed functions we studied earlier, we can generalize their end behavior. End Behavior of functions f (x) = axn , n odd. Suppose f (x) = axn where a = 0 is a real number and n ≥ 3 is an odd natural number. The end behavior of the graph of y = f (x) matches one of the following: a>0 a<0 Despite having different end behavior, all functions of the form f (x) = axn for natural numbers...
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