The left hand limit of  f at 0 is
–
2
2
0
0
lim
( )
lim
0
0
x
x
f x
−x
→
=→
=
=
The right hand limit of f at 0 is
0
0
lim
( )
lim
0
x
x
f x
x
+
+
→
=→
=
Thus 
lim0
( )
0
x
f x
→
=
= f(0) and hence f is continuous at 0 This means that f is
continuous at every point in its domain and hence, f is a continuous function Example 14 Show that every polynomial function is continuous Solution Recall that a function p is a polynomial function if it is defined by
p(x) = a0 + a1 x +