Coming up with an epsilon value

I'm having a little problem with this. Here is the problem statement: Quote:

Use the graph of the function f given in figure 3.21 to estimate a number epsilon such that: If 0 < |x - 1| < 0.5, then |f(x) - 1.5| < e. Find e.

Looking at the graph of the function, f(.5) is approx: .75, and f(1.5) is approx 1.75. So, within the desired interval the range of f(x) varies from .75 to 1.75. The correct answer is given as an epsilon = .75. Quote:

But if |f(x) - 1.5| < .75, then -.75 < f(x) - 1.5 < .75, and this would give a range of f(x) as (.75, 2.25), and 2.25 is well out of the range of the interval.

So I don't understand this answer at all.