7'2 Polynomial Functions and Their Graphs

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7.2 Polynomial Functions and Their Graphs
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Essential Question How can features of graphs be
used to solve mathematical and real-world
problems? Objectives Identify and describe
the important features of the graph of a
polynomial function. Use a polynomial function
to model real-world data.
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End Behavioris what a function is doing on the
left and right of the graph

• Leading coefficient positive degree odd
• Leading coefficient positive degree even
• Leading coefficient negative degree odd
• Leading coefficient negative degree even

• falls on left, rises on right
• rises on left, rises on right
• rises on left, falls on right
• falls on left, falls on right

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Describe the end behavior of each function.
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Local Maximum and Minimum

• f(a) is a local maximum (plural, local maxima) if
  there is an interval around a such that f(a) gt
  f(x) for all values of x in the interval, where x
  does not equal a.
• f(a) is a local minimum (plural, local minima) if
  there is an interval around a such that f(a) lt
  f(x) for all values of x in the interval, where x
  does not equal a.

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Local Maximum and Minimum

• In other words
• Local maxima are peaks
• Local minima are valleys

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For the following polynomial function, find any
local maxima or minima. Find the intervalsover
which the function is increasing and decreasing.
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For each polynomial function, find any local
maxima or minima. Find the intervalsover which
the function is increasing and decreasing.
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The world motor vehicle production,in thousands,
is given below.
a. Using x 0 for 1960, find a quartic
regression model for the data.
b. Use the model to estimate the production of
vehicles for the year 2001.
c. Using the model, when will the production of
motor vehicles be 0?