Use the key features of the polynomial f(x) = −2x3 + 5x2 − 2x − 3 to describe its end behavior. The left side continues down, and the right side continues up.
The left side continues down, and the right side continues down.
The left side continues up, and right side continues up.
The left side continues up, and the right side continues down.

 Choice D

The left side continues up, and the right side continues down.

In short, left = up & right = down

We can say "rises to the left and falls to the right" as an alternative phrasing.

==============================================================

Explanation:

The leading term is -2x^3 and this term directly affects the answer. No other term will play a role here. The leading term always has the largest exponent.

The variable portion x^3 has an odd exponent, so the end behavior indicates that one side will go up, and the other side goes down.

The leading coefficient is -2. The negative value here means as x gets larger, y gets smaller. Consider y = -2x^3. If x = 1 then y = -2. If x = 10, then y = -1000. And so on. I recommend making a table of values. The table will show that the graph is falling to the right. Or it's going downhill as we move to the right. That must mean the left side is going upward forever toward positive infinity.

In short, the right goes down while the left goes up.

If the leading coefficient was positive, then the right would go up and the left would go down.

The graph is below. Graphing the equation would quickly show the answer but I'm assuming your teacher is asking you to do this question without graphing. Which means you should use the logic discussed above. The graph is simply a verification tool. I used GeoGebra to make the graph.

last one.

step-by-step explanation:

last one.

generally speaking, the others follow some sort of pattern that correlates to either linear (looks like a straight line) or sinusoidal (looks like an s).

the last one is just a random cloud of points that doesn't correlate to any particular known order.

add an image

step-by-step explanation: