Continuity &
Discontinuity of
Functions

Continuity of
Functions
1.
Illustrate continuity of a function at a point;
2.
Determine whether a function is continuous at a point or
not;
3.
Illustrate continuity of a function on an interval; and
4.
Determine whether a function is continuous on an
interval or not.

Concept of
Continuity
Geometrically, the graph of a function is continuous if there
is no gap or break in the graph. That is, a function f is
continuous at a point where x= a if its graph passes through
the point with coordinates ( a, f(a)) without a break in the
line or curve.

Continuity of
Functions
a.
Continuity at a Point
Example #1
Example #2

a.
Continuity at a Point

a.
Continuity at a Point
Example #4:
Determine if f(x) = x
3
+ x
2
– 2 is continuous or not at x = 1.
Example #5:
Determine if f(x) =
is continuous or not at x = 0.
Example #6:
Determine if f(x) =
is continuous or not at x = 2.
Example #7
: Determine if
Is continuous or not at x = 4

b.
Continuity on an Interval

b.
Continuity on an Interval

b.
Continuity on an Interval
a. (-1 , 1)
continuous
b. (-
∞, 0)
continuous
c.
(0, +∞)
continuous

b.
Continuity on an Interval
a. (-1 , 1)
not
continuous
b.
[0.5 , 2]
continuous

b.
Continuity on an Interval

b.
Continuity on an Interval

b.
Continuity on an Interval

Seatwork