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4 days ago

What is the end behavior of the graph of the polynomial function f(x) = –x5 + 9x4 – 18x3?

Mathematics

2 answers:

tester [3.9K]4 days ago

6 0

Hint-

$f(x)=a_0+a_1x+a_2x^2+....+a_nx^n$

For the given function,

$Leading \ term=a_nx^n \, \ Leading \ coefficient=a_n \, \ degree = n$

Solution-

The polynomial provided,

$f(x) = -x^5+9x^4-18x^3$

$Leading \ term=-x^5 \, \ Leading \ coefficient=-1 \, \ degree = 5$

Being an odd-degree polynomial with a negative leading coefficient, the end behavior is as follows:

$As \ x \rightarrow -\infty,f(x)\rightarrow +\infty \ and \ x \rightarrow +\infty,f(x)\rightarrow -\infty$

Thus, the graph will occupy the 2nd and 4th quadrants.

Inessa [3.9K]4 days ago

5 0

Being an odd function, the "tails" extend in opposite directions. Additionally, since it’s a negative function, the left side begins at the upper left while the right descends into negative infinity. Conversely, if it were a positive function, the tails would face the opposite directions whereby the left side would rise from negative infinity while the right side ascends into positive infinity.

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