Question

Without graphing, describe the end behavior of the graph of the function. (Image provided includes function and answer options)

Answer 1

Answer:

A.

Step-by-step explanation:

Not sure how to show work; it's intuitive.

Think about it like this.

When x gets infinitely large, we want to know if the y-value gets larger or smaller.

Given this function, we know that f(x) approaches negative infinity when x gets larger because -(∞)³ would just be a really big negative number. (I'm plugging ∞ in for x because it just represents the idea that x is getting infinitely large.)

Similarly, we know that f(x) approaches positive infinity when x gets infinitely negative because -(-∞)³ would be a really big positive number; the negatives cancel out. (Again, I'm plugging ∞ in for x because it represents the idea that x is getting infinitely negative.)

Another way you could think about it is to visualize a negative cubic function. One end goes up and the other goes down. You know from algebra that when cubic functions are negative, they get bigger on the left and smaller on the right; this gives you the same answer.