Welcome to Clip from Spiral logo

Interactive video lesson plan for: How do you find discontinuities? (KristaKingMath)

Activity overview:

In this video we talk about how to find discontinuities in a function.

0:02 How do you find the discontinuities when you have a picture of the graph of the function? // You need to look for any point where there’s any kind of hole, break, jump, asymptote, or endpoint in the graph. These will all be discontinuities. If you’re tracing the graph from left to right, and you have to pick up your pencil to continue tracing, then there’s a discontinuity at that point. Endpoints are technically discontinuous because there’s only a one-sided limit on one side, which means there’s no general limit, which means the endpoint is technically discontinuous. In order for the function to be discontinuous at an asymptote, the curve needs to exist on both sides of the asymptote. If the curve only exists on one side of the asymptote, then there’s no discontinuity at that point.

1:32 How do you find the discontinuities of a rational function? // Rational functions are fractions with polynomials in the numerator and denominator. Any value that makes the denominator of the fraction 0 is going to produce a discontinuity. If the zero value can be canceled out by factoring, then that value is a point discontinuity, which is also called a removable discontinuity. If the zero value can’t be canceled out by factoring, then that value is an infinite discontinuity, which is also called an essential discontinuity. You can also think of this as just a vertical asymptote for the function.

2:52 How do you find the discontinuities of a piecewise defined function? // You can have discontinuities within each “piece” of the piecewise defined function, just like you could for any other kind of function. But piecewise functions can also be discontinuous at the “break point”, which is the point where one piece stops defining the function, and the other one starts. If the two pieces don’t meet at the same value at the “break point”, then there will be a jump discontinuity at that point. For that reason, jump discontinuities are really common for piecewise functions.

3:17 Summary

● ● ● GET EXTRA HELP ● ● ●

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

● ● ● CONNECT WITH KRISTA ● ● ●

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
TWITTER // https://twitter.com/KristaKingMath
INSTAGRAM // https://www.instagram.com/kristakingmath/
PINTEREST // https://www.pinterest.com/KristaKingMath/
GOOGLE+ // https://plus.google.com/+Integralcalc/
QUORA // https://www.quora.com/profile/Krista-King

Tagged under: find,educational,removable discontinuities,nonremovable,removable,discontinuities rational functions,piecewise function,discontinuities occur,find discontinuities,Krista King,detect discontinuities,find discontinuities graphs,calculus,rational function,locate discontinuities functions,discontinuities,locate discontinuities,find discontinuities 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 How do you find discontinuities? (KristaKingMath) on Google+ Share How do you find discontinuities? (KristaKingMath) on Twitter Share How do you find discontinuities? (KristaKingMath) on Facebook Pin How do you find discontinuities? (KristaKingMath) Email How do you find discontinuities? (KristaKingMath)

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.

Quickfire

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

Discuss

Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices

Clip

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

Spiral
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

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

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

Spiral
Review of Spiral by teacher: Miss Ord @ordmiss

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

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

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

Spiral
Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

Spiral
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