C lim 3 3 therefore the function is continuous at 4

(c) 𝑓(𝑐) = lim
𝑥→𝑐
𝑓(𝑥)
√3 = √3 , Therefore, the function 𝑓 is continuous at 𝑥 = 4 .
ACTIVITIES
Use your graphing notebook to answer the following.
Activity A. Given the graph on the side, determine if the function 𝑓(𝑥)
continuous at the following values of 𝑥
1. 𝑥 = −1
2. 𝑥 = −3
3. 𝑥 = −2
Activity B. Determine if the following functions are continuous at the given
value of 𝑥 . Show your complete solution using the three conditions of
continuity.
is
.
How will you determine if the function is continuous at a given number?

Need to Remember
Three conditions of Continuity
A function 𝑓(𝑥) is said to be continuous at 𝑥 = 𝑐 if the following three
conditions are satisfied:
(i) 𝑓(𝑐) exist;
(ii) lim
𝑥→𝑐
𝑓(𝑥) exist; and
(iii) 𝑓(𝑐) = lim
𝑥→𝑐
𝑓(𝑥)
If at least one of these conditions is not met, 𝑓 is said to be discontinuous
at 𝑥 = 𝑐 .
VALUING
In mathematics, a continuous function is a function that does not have any
abrupt changes in value, known as discontinuities. More precisely,
sufficiently small changes in the input of continuous functions result in
arbitrary small changes in its output. If not continuous , a function is said
to be discontinuous.
In life, problems are what make life worth living. They help us adapt to
become tougher as we adapt to different situations. Just continue to live and
focus positively whatever problem you are facing because it has always a
solution. Therefore, never allow your challenges to stop you from fulfilling
your true potentials in life.

POSTTEST
Give the correct answer.
Determine if the given functions 𝑓(𝑥) are continuous or not at the given
value of 𝑥. Show your complete solution.
1. 𝑓(𝑥) = 𝑥
2
+ 2𝑥 + 1 at 𝑥 = 2
Answer:__________________

KEY TO CORRECTION
REFERENCES
BOOK
Cuaresma, Genaro A. et al. 2004. Analytic Geometry and Calculus 1: A
Worktext for Math 26 . Los Baños, Laguna: Institute of Mathematical
Sciences and Physics, University of the Philippines.
Department of Education-Bureau of Learning Resources. 2016. Precalculus
Learner's Material.
Leithold, Louis. 1989. College Algebra and Trigonometry. Addison Wesley
Longman Inc., reprinted by Pearson Education Asia Pte. Ltd., 2002.
PRETEST POSTTEST
1. CONTINUOUS 1. CONTINUOUS
2. CONTINUOUS 2. CONTINUOUS
3. DISCONTINUOUS 3. CONTINUOUS
4. DISCONTINUOUS 4. DISCONTINUOUS
5. CONTINUOUS 5. DISCONTINUOUS
ACTIVITIES
A. 1. CONTINUOUS B. 1. CONTINUOUS
2. CONTINUOUS 2. CONTINUOUS
3. DISCONTINUOUS 3. DISCONTINUOUS

S
ENIOR
H
IGH
S
CHOOL
Continuity of a Function
on an Interval
Module
7
Quarter 3
Basic Calculus

EXPECTATION
Lesson: Continuity of a Function on an Interval
Learning Objective:
At the end of the learning episode, you are expected to: