Example 3 (a) Find where

1
Example 3 (a) Find where
Solution The graph of f below looks like two
horizontal dotted lines on y0 and y1. Hence
for any number c there are rational numbers x/
arbitrarily close to c where f(x/)1 and
irrational numbers x// arbitrarily close to c
where f(x//)0. Hence does
not exist for any number c.
2
(b) Find where
Solution The graph of g below looks like two
dotted lines on y0 and yx. Hence for any
nonzero number c there are rational numbers x/
arbitrarily close to c where g(x/)x/ and
irrational numbers x// arbitrarily close to c
where g(x//)0. Hence does
not exist when c is nonzero. However, the
lines y0 and yx intersect at the origin. Hence
exists and equals 0.