In general, the "end behavior" is a description of what graph will do when you work with really large positive and negative numbers, so as x -> infinity and as x -> –infinity.
The way to figure this out is to find the highest degree term. In your exercise, that's the –2x^4. When you deal with really large numbers, only this term will matter, because it will overpower the impact of any lower degree term. So you can think of this function really looking like y = –2x^4 once you are away from the y-axis.
In general, as x gets huge in a positive way, as x -> infinity, the y-values of this will get big in a negative way, f(x) -> –infinity.
In general, as x gets huge in a negative way, as x -> –infinity, the y-values of this will also get big in a negative way, f(x) -> –infinity.
See the attached graph of y=-2x^2 (red) and the graph of your function. These are zoomed out, so you're looking at what's happening on the edges.
Notice the graphs basically look the same when viewed from this perspective.
