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ACTIVITY 6.2
Using Technology
Setting a Good
Viewing Window
Graphing Calculator Activity for use with Lesson 6.2
When you graph a polynomial function with a graphing calculator, you must
choose a viewing window that displays the important characteristics of the
graph. Use what you know about end behavior to find such a viewing window.
EXAMPLE
Graph ƒ(x) = 0.2x3 º 5x2 + 38x º 97.
INT
STUDENT HELP
NE
ER T
KEYSTROKE
HELP
SOLUTION
1 Graph the function using the
standard viewing window.
See keystrokes for
several models of
calculators at
www.mcdougallittell.com
º10 ≤ x ≤ 10, º10 ≤ y ≤ 10
2 Adjust the horizontal scale and the vertical scale until you see the graph’s
end behavior and any points where it turns. A good viewing window for this
graph is º10 ≤ x ≤ 20 and º20 ≤ y ≤ 10.
º10 ≤ x ≤ 20, º10 ≤ y ≤ 10
º10 ≤ x ≤ 20, º20 ≤ y ≤ 10
EXERCISES
Find intervals for x and y that describe a good viewing window for the graph of
the polynomial function.
1. ƒ(x) = x3 + 6x2 º 11x + 3
2. ƒ(x) = ºx3 + 25x2 + 4
3. ƒ(x) = x4 º 5x2 + 6
4. ƒ(x) = ºx4 º 3x3 + x2 º x + 5
5. ƒ(x) = ºx5 + 5x3 º 4x + 10
6. ƒ(x) = x5 º 10x4 + 35x3 º 50x2 + 24x
7.
EDUCATION For 1983 to 1996, the amount P (in millions of dollars) spent
by public elementary and secondary schools and the amount R (in millions of
dollars) spent by private elementary and secondary schools can be modeled by
P = 11.7x4 º 340x3 + 2931x2 + 1560x + 182,000
R = 0.422x4 º 9.84x3 + 44.9x2 + 779x + 15,900
where x is the number of years since 1983. Find intervals for the horizontal
and vertical axes that describe a good viewing window for the graphs of both
functions. Source: U.S. National Center for Education Statistics
6.2 Technology Activity
337