# C lim 3 3 therefore the function is continuous at 4

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(c)𝑓(𝑐) = lim𝑥→𝑐𝑓(𝑥)√3= √3,Therefore, the function𝑓iscontinuousat𝑥 = 4.ACTIVITIESUse your graphing notebook to answer the following.Activity A. Given the graph on the side, determineif the function𝑓(𝑥)continuous at the following values of𝑥1.𝑥 = −12.𝑥 = −33.𝑥 = −2Activity B. Determine if the following functions are continuous at the givenvalue of𝑥. Show your complete solution using the three conditions ofcontinuity.is.
How will you determineif the function is continuous at a given number?
Need to RememberThree conditions of ContinuityA function𝑓(𝑥)is said to be continuous at𝑥 = 𝑐if the following threeconditions are satisfied:(i)𝑓(𝑐)exist;(ii)lim𝑥→𝑐𝑓(𝑥)exist; and(iii)𝑓(𝑐) = lim𝑥→𝑐𝑓(𝑥)If at least one of these conditions is not met,𝑓is said to bediscontinuousat𝑥 = 𝑐.VALUINGIn mathematics, a continuous function is a function that does not have anyabrupt changes in value, known as discontinuities. More precisely,sufficiently small changes in the input of continuous functions result inarbitrary small changesin its output. If not continuous , a function is saidto be discontinuous.In life, problems are what make life worth living. They help us adapt tobecome tougher as we adapt to different situations. Just continue to live andfocus positively whatever problem you are facing because it has always asolution. Therefore, never allow your challenges to stop you from fulfillingyour true potentials in life.
POSTTESTGive the correct answer.Determine if the given functions𝑓(𝑥)arecontinuous or not at the givenvalue of𝑥.Show your complete solution.1.𝑓(𝑥) = 𝑥2+ 2𝑥 + 1at𝑥 = 2
KEY TO CORRECTIONREFERENCESBOOKCuaresma, Genaro A. et al. 2004.Analytic Geometry and Calculus 1: AWorktext for Math 26. Los Baños, Laguna: Institute of MathematicalSciences and Physics, University of the Philippines.Department of Education-Bureau of Learning Resources. 2016.PrecalculusLearner's Material.Leithold, Louis. 1989.College Algebra and Trigonometry.Addison WesleyLongman Inc., reprinted by Pearson Education Asia Pte. Ltd., 2002.PRETESTPOSTTEST1. CONTINUOUS1. CONTINUOUS2. CONTINUOUS2. CONTINUOUS3. DISCONTINUOUS3. CONTINUOUS4. DISCONTINUOUS4. DISCONTINUOUS5. CONTINUOUS5. DISCONTINUOUSACTIVITIESA.1. CONTINUOUSB. 1. CONTINUOUS2. CONTINUOUS2. CONTINUOUS3. DISCONTINUOUS3. DISCONTINUOUS
SENIORHIGHSCHOOLContinuity of a Functionon an IntervalModule7Quarter 3Basic Calculus
EXPECTATIONLesson: Continuity of a Function on an IntervalLearning Objective:At the end of the learning episode, you are expected to:

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