Use the given graph of f to find a number δ such that

Question

if
0 < |x − 3| < δ then |f(x) − 2| < 0.5.

since i cannot put up the graph ill put the coordinates
(2.6,1.5)
(3,2)
(3.8,2.5)

Please help im not sure how to solve this

Answer 1

Is the graph piecewise straight segments? If so, then since the two segments have different slopes near (3,2) you need to pick the segment with the smaller slope, since that will produce a larger value of δ to make |f(x)-2| < 0.5