Use the definition of continuity to find the constant such that the function is continuous f(x) = x+3, x<-1 2x-c, x>-1

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Use the definition of continuity to find the constant such that the function is continuous f(x) = x+3, x<-1 2x-c, x>-1

MIT 18.01 Single Variable Calculus (OCW)
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FOR A FUNCTION TO BE CONTINUOS, THE LIMIT AS x TENDS TO -1 FROM THE LEFT MUST BE EQUAL TO THE LIMIT AS x TENDS TO -1 FROM THE POSITIVE DIRECTION. the limit when x<-1 is 2 and the limit when x>-1 is -2-c , the function can only be continuos if the two are equal so we equate them 2=-2-c c=-4 the constant must be -4 so for the function to be continuos, we redefine it to look like f(x)=x+3.x<-1 2x+4, x>-1
For a function (line of curve) to be continuous at a point, the limit to the point from both the sides have to be equal. For example, this is a continuous function |dw:1349597541245:dw| and this is not |dw:1349597628198:dw| Coming to your problem, if we want your function to be continuous X --> -1 from right has to be equal to X--> -1 from the left X + 3 = 2X - C Here, X= -1 There for -1 + 3 = 2 (-1) - C 2 = -2 - C Therefore, C = -4 So, the function is redefined as f(x)=x+3. x < -1 2x+4, x > -1
AbbasBagwala .fellow mathmatician your 1st curve looks like a REMOVABLE DISCONTINUITY CURVE

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