Basic Cal

1. 1
Continuity of a
function
WK3

2. 2
Objectives
 Illustrate continuity of a
function at a number;
 determine whether a function
is continuous at a number or
not; and
 illustrate continuity of a
function on an interval.

3. 3
Continuous vs Not Continuous
 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 break in the line or
curve.

4. 4
Continuous vs Not Continuous
 If the function f(x) is not continuous at x=a, we can say
that f is discontinuous at x=a and the point (a, f(a)) is
called the point of discontinuity.

5. 5

6. 6
Continuity of a Function at a Number

7. 7
Examples:

8. 8
x y x y
1 6 2.1 16.34
1.99 14.8704 2.01 15.1304
1.999 14.987004 2.001 15.013004
1.9999 14.99870004 2.0001 15.00130004

9. 9

10. 10
Examples:

11. 11
Continuity of a Function on an Interval

12. 12
 A function is said to be
continuous on an interval
when the function is defined
at every point on that
interval and undergoes no
interruptions, jumps or
breaks.

13. 13

14. 14
EXAMPLE
X-values Y-values
-3.9 1.71
-3 0
-2.5 -0.25
-2 0
-1.0001 1.99970001
Based from the table, all domains in between (-4,-1) has its own defined y-value.
Therefore, we can say that it is continuous on the open interval (-4,-1)

15. 15
EXAMPLE
right

16. 16
EXAMPLE
-1

17. 17

18. 18
EXAMPLE
Based on the table, all domains (x-values) in between (-4 to 1) has its own defined
y-value except -3.9. Therefore, we can say that it is not continuous on the open
interval (-4, 1).
x-values y-values
-3.9 Imaginary number
0 1.732050808
0.9999 1.999749984

19. 19

20. 20

21. 21

22. 22