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Sketch the graph of a function $ f $ that is continuous except for the stated discontinuity.

Discontinuities at -1 and 4, but continuous from the left at -1 and from the right of 4

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Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

Okay, this problem, we have a function F. Of X. And we want to graph an example what F of X might look like if it's discontinuous at the number negative one And just continuous at the # four. Yeah, we also wanted to be continuous as we come into negative one from the left, And we wanted to be continuous as we come in to the # four from the right. So if we're continuous coming into negative one from the left, just a nice curve like this, but now we have a discontinuity um and we'll take care of the middle part between negative one and four in a minute. We do want to function also to be continuous um as X approaches for coming in from the right. Um So we could have something that looks like this, It's going to be discontinuous at -1 and four. And uh so well we can stay with the same color, but if we want to dis continuity at negative one, um let's make this an open circle and let's have the function pick up Down here when X is -1. And we can have it uh From here we can have it move up if we want and be discontinuous. Uh not defined. This piece is not defined at four, whereas this piece will be all right. Let's take a little look at our graph and make sure we satisfied all to continue all the conditions. You can clearly see that the function F of X is discontinuous when X is negative one. Um You open circle means you don't have the point here when X is negative one, but it filled in circle means you do have it here. So you do have this continuity when X is negative one. And clearly you have another discontinuity when X is for We wanted to function to be continuous coming in from the left of -1. It is and we wanted to function to be continuous coming in from the right side of four. It is

Temple University