If we graph the functions x2 and 2x, they intersect in three places:
One of the points of intersection has a negative value of x, and two have positive values of x. After those intersections, as x approaches ∞ the graph of 2x will always be on top of the function x2.
Here are some values of the two functions. We can see that when x = 2 and x = 4 the functions intersect, and that when x is greater than 4 the function 2x is pulling away from the function x2. It's like a horse race, where the function x2 is not having a good day.
If we take these values and look at the quotient , here's what happens:
We're already down to about 0.098 when x = 10, and we've barely started! When x = 100, we're down to