SOLUTION: y=|x−3|+|x+2|−|x−5|, if 3<x<5

Question 1153233: y=|x−3|+|x+2|−|x−5|, if 3

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

You have not posted a question.... I will assume you want a graph.

In any function like this, every segment of the graph is linear; and the general behavior of the graph changes only at the critical points -- where one of the terms is 0.

So the behavior of the graph of this function changes only at -2, 3, and 5. And since the specified interval is from x=3 to x=5, the graph on that interval is linear.

Determine the linear function on that interval using the function values at the two endpoints of the interval:

The linear equation with a graph passing through (3,3) and (5,9) is y = 3x-6.

Here is a graph of the given function and the line y=3x-6 on the interval (2,6),showing that the two functions are equivalent on the interval (3,5):

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