Determine the end behavior: f(x)= -12x^8 - 21x^5 -22

Mathematics
Tutor: None Selected Time limit: 1 Day

I don't understand how to find end behavior

May 26th, 2015

"Determine end behavior"  means "Find where the function going as you advance on the negative and on the positive x-axis" or equivalently "What is the behavior of the function as x -> - infinity or as x -> + infinity"

To this - we consider that as the absolute value of x goes to large numbers, every polynomial function behavior  is dominated by the highest power. In this case the function f(x) -> -12x^8 as x-> - infinity or x-> + infinity

The term -12x^8 is always negative irrespective of the sign of x and goes to very large  negative numbers in either x-> - infinity or x-> + infinity, case. Thus

f(x) -> - infinity on both x-> - infinity and x-> + infinity is the answer.

Good Luck!

May 26th, 2015

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