Answer:
Down.
Step-by-step explanation:
ƒ(x) = 3x³ - x² + 4x - 2
"They" are asking you to determine the end behaviour of the function, that is, what happens to the function as x ⟶ -∞.
The important point to remember is that, when x is large enough, the term of highest degree (the x³ term) will be so large that you can ignore all the other terms.
If x is large and negative,
f(x) ≈ 3(-x)³ = 3(-1)³(x)³= -3x³
Thus, the graph is in the third quadrant and the graph points down.
The figure below shows the graph of your function. It points sharply down on the left-hand side.
