How do you find the end behavior of $P(x) = 3x^7 + 5x^2 - 8$ ?

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Answer 1 · 2015-05-03T16:03:45

The end behavior of a function is the behavior of the function as x approaches positive infinity or negative infinity.

So we have to do these two limits:

$lim_(xrarr-oo)f(x)$

and

$lim_(xrarr+oo)f(x)$ .

Than:

$lim_(xrarr-oo)(3x^7 + 5x^2 - 8)=lim_(xrarr-oo)(3x^7)=-oo$

and

$lim_(xrarr+oo)(3x^7 + 5x^2 - 8)=lim_(xrarr+oo)(3x^7)=+oo$ .

This is because the power $3x^7$ is the highest power and its behavior is the same of the whole function.

How do you find the end behavior of P(x) = 3x^7 + 5x^2 - 8P(x) = 3x^7 + 5x^2 - 8?