Answer: A) The degree of the polynomial is even
We can determine this by noticing that the end behavior is different on both sides. The left end goes downward while the right end goes upward. This opposing nature indicates we have an odd degree function like a cubic. If this was an even degree function, then the left end must also point upward to mirror the right end. That's why choice A is the final answer.
Choice B can be ruled out since it's a true statement. This is because the right end behavior goes to positive infinity. Such end behavior is tied to positive leading coefficients (whether even or odd functions, it doesn't matter).
Choice C is also true and can be ruled out because this function curve does have one relative minimum. It's the location where the curve bottoms out in the valley at around x = 3.5 or so. It's the lowest point in the neighborhood/interval of points.
Choice D can be ruled out for similar reasons as choice C, except this time we're looking at the highest point in a certain neighborhood. That highest point occurs somewhere between x = 1.5 and x = 2 where the peak of the hill is located.
To rephrase those last three paragraphs: choices B through D are true statements, so they can be ruled out.
