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# Sketch the graph of a function $f$ that is continuous except for the stated discontinuity. Discontinuous, but continuous from the right, at 2.

## The graph of $y=f(x)$ must have a discontinuity at$x=2$ and must show that $\lim _{x \rightarrow 2^{+}} f(x)=f(2)$

Limits

Derivatives

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

Okay in this problem we want to graph a function F of X that is uh discontinuous at two. So the function is going to be discontinuous at two, but it is going to be continuous from the right at two. So in other words, as X is approaching two from the right side, the function is continuous lift draw um a possible function in blue. So Coming in from the right, X is approaching two, It's continuous from the right side at two. So that means uh that the function is to find at two. Um and continuous set to so as to function um the limit of the function as X approaches to equals the value of the function at two. So here's the function continuous from the right at two, But overall the function is discontinuous at two. so for X values to the left of two, we wanted this continuity at two. So let's put an open circle here above X equals two and let's continue DeGraff for X values. Uh less than two. So here is a function F of X. Discontinuous set to, But it was continued continuous from the right at two.

Temple University

#### Topics

Limits

Derivatives

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp