Welcome to Clip from Spiral logo

Interactive video lesson plan for: Jump discontinuities - What are they?

Activity overview:

► My Limits & Continuity course: https://www.kristakingmath.com/limits-and-continuity-course

In this video we’re talking about jump discontinuities, or discontinuities of the first kind. These kinds of discontinuities are big breaks in the graph, but not breaks at vertical asymptotes (those are specifically called infinite/essential discontinuities). You’ll often see jump discontinuities in piecewise-defined functions. A function is never continuous at a jump discontinuity, and it’s never differentiable there, either.

Skip to section:

0:18 // What are jump discontinuities? What are they compared to infinite/essential discontinuities?
0:52 // The general limit will never exist at a jump discontinuity
1:59 // What’s going on at x=-2?
4:46 // What’s going on at x=3?
7:05 // What’s going on at x=5?
8:22 // How to find the value of the function at a jump discontinuity

When you’re looking at the behavior of a function at a jump discontinuity, you already know that the general limit doesn’t exist, that the function isn’t continuous, and also that it’s not differentiable. Which means that all you really have left to investigate are the one-sided limits, and the actual value of the function at that point.

The one-sided limits will never be equal if it’s a jump discontinuity, so you want to look at the left-hand limit by tracing the function from the left, or negative side, and identifying the y-value where you run out of graph. You also want to trace the function from the right, or positive side, and identify the y-value where you run out of graph. This will give you the left- and right-hand limits, respectively.

You'll also want to see where the graph has a "filled in" circle. It might be connected to the left piece of the graph, or to the right piece of the graph, or it might be floating somewhere else along the vertical line where the jump discontinuity exists. Regardless of where it is, the filled in circle represents the function's actual value at that point.

Music by Joakim Karud: http://soundcloud.com/joakimkarud

● ● ● GET EXTRA HELP ● ● ●

If you could use some extra help with your math class, then check out my website // http://www.kristakingmath.com


Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com

FACEBOOK // https://www.facebook.com/kristakingmath/
INSTAGRAM // https://www.instagram.com/kristakingmath/

Tagged under: find jump discontinuities, jump discontinuities,jump discontinuity,jump discontinuities,discontinuity kind,break discontinuity,discontinuities,-sided limits,left-hand limit,-hand limit, function,limits,calculus

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

Play this activity

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

Share on:

Share Jump discontinuities - What are they? on Google+ Share Jump discontinuities - What are they? on Twitter Share Jump discontinuities - What are they? on Facebook Pin Jump discontinuities - What are they? Email Jump discontinuities - What are they?

Ready to see what else Spiral logo can do?

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.


Carry out a quickfire formative assessment to see what the whole class is thinking


Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices


Turn any public video into a live chat with questions and quizzes

1000s of teachers use Spiral to deliver awesome, engaging activities that capture students' understanding during lessons.

Now it's your turn Sign up

Spiral Reviews by Teachers and Digital Learning Coaches

Review of Spiral by teacher: Kathryn Laster @kklaster

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech

Review of Spiral by teacher: Room 220 Math Stars @3rdgradeBCE

Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

Review of Spiral by teacher: Miss Ord @ordmiss

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral

Review of Spiral by teacher: Adam J. Stryker @strykerstennis

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!

Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

Review of Spiral by teacher: Brett Erenberg @BrettErenberg

The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed!

Get the Clip Chrome Extension & Create Video Lessons in Seconds

Add Clip to Chrome