Question

Let f(x)= -3x^4+79x^2-3x+1
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5x^4+19x^4+2x+5

Discuss the short run behavior for f(x)and the long run for f(x).

Answer 1

did you not check on previous replies to your previous questions?

see:

http://www.jiskha.com/display.cgi?id=1197011555

Answer 2

I think you meant to write 19x^3, not 19x^4, in the denominator

As x-> +infinity or -infinity, f(x) approaches an asymptote of -3/5

At x=0, it equals 1/5. In the region "near" x=0, there are some wild oscillations, and probably a few crossings of the x axis (where the numerator equals zero). There may be some singularities (infinities)in a negative-x region were the denominator is zero.

I suggest you do some plotting of the function yourself.