Question

Which function displays this end behavior

Answer 1

Step-by-step explanation:

Since you haven't provided any functions, I can answer this question generally as to what the function would look like.

So when a polynomial has an even degree, then the two end behaviors will go in the same direction, and when it has an odd degree, then the two end behaviors will be in opposite directions. When a polynomial has a positive leading coefficient the right side will go towards infinity, and if a polynomial has a negative leading coefficient the right side will go towards negative infinity.

So let's look at the information:

As x approaches negative infinity, y approaches positive infinity.

Just given this we can't really say anything about the polynomial since we have to relate this to the right end behavior, or as x approaches infinity, so let's look at that.

As x approaches positive infinity, y approaches negative infinity.

This means that as x increases, y decreases, so that means the leading coefficient is negative. Since we know both end behaviors, and they're opposite (one y-value goes to negative infinity, and the other positive infinity), that means the polynomial is an odd degree.

So this means the polynomial will look something like this:

$ax^n+bx^{n-1}+cx^{n-2}...$

where the leading coefficient "a" is negative and the degree of the polynomial (degree of leading coefficient) will be odd.