Finding a Limit
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Find limit x>> -1^+ f(x)
f(x)= x - 2, for x <= 3; x - 1, for x > 3
Also: When you first begin to draw the graph of f(x), why do you start where you do? How high do I go when drawing a graph? How do I know when to stop?
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Solution Summary
The solution explains how to find the limit of the function and how to graph the function in a meaningful way.
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We want to find the limit of f(x) as x approaches -1 from the right. (Limit x  -1 means that we're looking at what happens to f(x) as x approaches -1, and the + next to the -1 means we're interested in the limit from the right, not from the left.)
f(x)= x - 2, for x ≤ 3; x - 1, for x > 3
Let's draw the graph first, then we can use the graph to find the limit. I'll tell you what I'm doing step-by-step.
We know that f(x) = x - 2, for x ≤ 3. Because this is valid for all values of x less than 3 AND when x = 3, we might as well start with x = 3. Plug x = 3 into the equation: f(3) = 3 - 2 = 1. Therefore, there is a point at (3, 1). Draw that on the graph. (I'm trying to be as accurate as possible. If you make a graph by hand it will probably look better.)
Now, look at ...
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