Question

Can you please explain to me what the end behavior of the function f(x)=-2x^4-x^3+3 looks like?

Answer 1

The dominant term is -2x⁴. 

As X approaches infinite, y is naturally going to be really large as well.

Remember that a number with an even exponent, regardless of whether it's positive or negative, will be positive.
As x approaches infinite, y will approach -2 * ∞, or -∞. Therefore, the end behavior in the positive direction is y=-∞
As x approaches negative infinite, y will approach -2 *∞ again. This is because         -∞⁴ = ∞. Therefore, the end behavior in the negative direction is also y=-∞

Basically, due to the dominance of the -2x^4 term, the function will look more or less like a downward facing parabola with a y-intercept of 3.