Question

What does the end behavior look like of the graph of the function f(x)=-8x^4-2x^3+x?

I know what the graph itself looks like but I have trouble explain its end behavior.
Thank you.

Answer 1

In this question, the highest power is x^4 which is an even number. In this case, the f(x) will be same for plus X or minus X.
The coefficient is -8 which is a minus. In this case, the f(x) will become minus:

The result would be:
when X go the left end(X= -∞), the f(x) will become minus (f(x)→−∞)
f(x)→−∞, as x→−∞

when X go the right end(X= +∞), the f(x) will become minus (f(x)→−∞)
f(x)→−∞, as x→+∞