Question

What is the end behavior of `y = 4x^2 + 9 - 5x^4 - x^3`?

Answer 1

As `x ->` negative infinity, `y ->` negative infinity and as `x->` positive infinity, `y->` negative infinity.

Explanation:

The degree (highest exponent) of this polynomial is 4, thus it is an even function. The end behavior of an even function is that the "ends" point in the same direction, either both up or both down.

The leading coefficient is -5, a negative number. Even functions with a negative leading coefficient have "ends" which both point down.

So, the end behavior is that both ends point down. This is expressed mathematically as follows:

As x approaches `-oo`, y approaches `-oo`.

As x approaches `+oo`, y approaches `+oo`

OR

As `x -> -oo`, `y->-oo`

As `x->+oo`, `y->-oo`