
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Transcribed Image Text:4. Fill in the blanks in the following table to summarize what you have discovered about the
end behavior of odd- and even-degree functions.
Odd-degree function
Positive leading
coefficient
Negative leading
coefficient
as x→∞, y →→
as x→∞, y →
as x→∞, y →→
as x→∞o, y →
as x→ ∞, y →→
Even-degree function
as x→∞, y →
as x→∞, y →→
as x→→∞, y →
as x→∞, y →
5. Describe the end behavior of each of the following polynomial functions.
A. y=x¹0 +5x²-3
|10
B. y=-2x5-4x² + x
as x→∞, y →
as x→∞, y.
as x→→∞, y →

Transcribed Image Text:2. The greatest exponent of an odd-degree function is odd. Examples of odd-degree functions
are y=x+ 6, y = 2x³, and y = x². In the Gizmo, experiment with functions of degree 1 and 3.
A. Fill in the blanks to show what happens to y as x approaches infinity or negative
infinity when the leading coefficient of an odd-degree function is positive.
as x→∞, y →
B. Fill in the blanks to show what happens to y as x approaches infinity or negative
infinity when the leading coefficient of an odd-degree function is negative.
as x→∞, y →→
as x→∞o, y →→
as x→∞, y →
3. The greatest exponent of an even-degree function is even. Examples of even-degree
functions include y = 3x², y = x^² - 5x³ +8, and y = 2x³ + x5-x. In the Gizmo, experiment
with functions of degree 2 and 4.
A. Fill in the blanks to show what happens to y as x approaches infinity or negative
infinity when the leading coefficient of an even-degree function is positive.
as x→∞, y →
as x→∞, y →
B. Fill in the blanks to show what happens to y as x approaches infinity or negative
infinity when the leading coefficient of an even-degree function is negative.
as x→∞, y →→
as x→→∞, y →→
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