If f (x) = - (1/x^3) and x takes on successive values from - 10 to 0.1,

a) f (x) increases throughout

b) f (x) decreases throughout

c) f (x) increases, then decreases

d) f (x) decreases, then increases

Alright, this one is a little interesting ... Let's perform some tests to figure out what is happening:

f (-10) = - (1 / (-10) ^3) = - (1/-1000) = 1/1000 (positive)

f (-5) = - (1 / (-5) ^3) = - (1/-125) = 1/125 (positive, bigger than the last one)

f (-1) = - (1 / (-1) ^3) = - (1/-1) = 1 (positive, bigger than the last one)

f (-0.1) = - (1 / (-0.1) ^3) = - (1/-0.001) = 1/0.001 = 1000 (positive, bigger than the last one)

f (0) = - (1/0^3) = undefined!

f (0.1) = - (1 / (0.1) ^3) = - (1/0.001) = - 1/0.001 = - 1000 (negative)

f (1) = - (1/1^3) = - (1/1) = - 1 (negative, but bigger than last one)

It's a little confusing with the undefined part at x = 0. What I can say is this, it is increasing from - 10 up to 0, something weird happens at 0 and it resets, and starts increasing from 0 up to 0.1.

I guess A would be the best answer?