Question

The function x^3-3x^2+2x rises as x grows very small.

The function 3x^3+x^2+2x rises as x grows very large

I have them both graphed.. but I don't quite understand

They're both True and False questions.

Answer 1

For the first question:
As x approaches 0 (very small) what happens to the value of the function (y), with the function being defined as y = x^3 - 3x^2 + 2x. If you have this graphed you should see that as we approach zero the value of y, counted on the y-axis grows smaller. Therefore we know that the first function does not rise as x grows very small.
For the second question:
Apply the same logic. Look at the graph. Now instead of x approaching zero, it is no approaching infinite (very large). Correspondingly, as x increases, the value of y increases and thus the function is said to have a positive slope or as the question says: it is rising.

Answer 2

Thank you very much!