Algebra 2 Name:
7.2 Notes Date:
· The end behavior of a polynomial function’s graph, is the behavior of the graph as x approaches negative infinity (______) or positive infinity (______).
· To determine what the graph of a polynomial function looks like, we look at the degree and the end behavior.
For the following graphs, give the degree and the end behavior:
degree:______degree:______degree:______degree:______
As xè-∞,f(x)è ____ As xè-∞,f(x)è____ As xè-∞,f(x)è____ As xè-∞,f(x)è____
(to the LEFT) (to the LEFT) (to the LEFT) (to the LEFT)
As xè∞,f(x)è____ As xè∞,f(x)è____ As xè∞,f(x)è____ As xè∞,f(x)è____
(to the RIGHT) (to the RIGHT) (to the RIGHT) (to the RIGHT)
· xè-∞ or xè∞ describes where you are on a graph in terms of the x-value. Thus, xè-∞ is talking about the LEFT side of the graph, and xè∞ is talking about the RIGHT side of the graph.
· f(x)è-∞ or f(x)è∞ describes where you are in terms of the y-values. Thus, f(x)è-∞ is talking about going DOWN on a part of the graph, and f(x)è ∞ is talking about going UP on a part of the graph.
Examples: Sketch the polynomial based on the degree and end behavior and describe the end behavior.
Ex. 1) f(x) = -5x2 Ex. 2) f(x) = 2x3 Ex. 3) f(x) = -4x
as , ______ as , ______ as , ______
as , ______ as , ______ as , ______
In addition to end behavior, we also describe graphs by stating their local maximum, local minimum, intervals when increasing and intervals when decreasing.
a) Where does the function have a local max?
b) Where does the function have a local min?
c) When is the function decreasing?
d) When is the function increasing?
Ex 1. Calculate the local maximum, local minimum, zeros, when the function is increasing,
when the function is decreasing, and the end behavior of the polynomial:
y = x3 + 4x2 + x – 6
local maximum: ( )
local minimum: ( )
zeros: ( ), ( ), ( )
End behavior:
as , ______ and as , ______
Increasing interval(s):
Decreasing interval(s):
Ex 2. Calculate the local maximum, local minimum, zeros, when the function is increasing,
when the function is decreasing, and the end behavior of the polynomial:
local maximum: ( )
local minimum: ( )
zeros: ( ), ( ), ( )
End behavior:
as , ______ and as , ______
Increasing interval(s):
Decreasing interval(s):
Try This: The number of business and pleasure travelers (in thousands) to the United
States from Canada is given in the table below for certain years. Use your graphing
calculator to find a quartic regression model for the data by using x = 0 for 1980.
1985 / 1989 / 1990 / 1991 / 1992 / 1993 / 1994 / 199510,721 / 15,325 / 17,263 / 19,113 / 18,596 / 17,293 / 14,970 / 13,668
HW: p.438 #’s 11, 14, 19, 22, 23, 29, 32, 35, 37, 43