\text { Consider the function } f(x)=(x-2)^{n} (a) Use a graphing utility to graph $f$ for $n=1,2,3$, and 4 . Use the graphs to make a conjecture about the relationship between $n$ and any inflection points of the graph of $f$.(b) Verify your conjecture in part (a).

\text { Consider the function } f(x)=(x-2)^{n} (a) Use a graphing utility to graph $f$ for $n=1,2,3$, and 4 . Use the graphs to make a conjecture about the relationship between $n$ and any inflection points of the graph of $f$.(b) Verify your conjecture in part (a).

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 83E

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\text { Consider the function } f(x)=(x-2)^{n}

(a) Use a graphing utility to graph $f$ for $n=1,2,3$, and 4 . Use the graphs to make a conjecture about the relationship between $n$ and any inflection points of the graph of $f$.
(b) Verify your conjecture in part (a).

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