A intermediate value theorem question

If f(x) = x^3 - 8x + 10, show that there are values c for which f(c) equals a) pi, b) - square root of 3, c) 5,000,000.
I understand the theorem, but I'm not sure how to show that without drawing a graph or solving the equation, and I'm pretty sure I'm not supposed to do either. Any help would be greatly appreciated!!!!

The great thing about the intermediate value theorem is that you don't need to solve directly. Graphing may help in general, but in this case, it's a cubic, so you should know enough about the graph to answer the question without graphing it. To show the existence of f(c) equal to anything, we just have to find some f(x) that's lesser and some f(y) that's greater (it doesn't matter which, because f is everywhere continuous). Since we are dealing with a cubic, this is always possible, because one side goes to infinity and the other goes to -infinity. In fact, let's prove all three at once:

f(1,000) = 1,000,000,000 - 8,000 + 10 = 999,992,010
f(-10) = -1,000 + 80 + 10 = -910

All of the numbers in the question lie between these values, thus proving that three values exist between -10 and 1,000 that map to them.