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

Question

1631 views around the world

You can reuse this answer
Creative Commons License

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.