Algebra: Piecewise Function Review

Greetings, today’s post is for those in need of a piecewise function review!  This will cover how to graph each part of that oh so intimidating piecewise function.  There’s x’s, there are commas, there are inequalities, oh my! We’ll figure out what’s going on here and graph each part of the piecewise-function one step at a time.  Then check yourself with the practice questions at the end of this post. Happy calculating! 🙂

 

Wait, what are Piece-Wise Functions? Exactly what they sound like! A function that has multiple pieces or parts of a function.  Notice our function below has different pieces/parts to it.  There are different lines within, each with their own domain.Screen Shot 2020-07-21 at 10.01.59 AM

Now let’s look again at how to solve our example, solving step by step:

Screen Shot 2020-07-21 at 10.02.29 AM.pngScreen Shot 2020-07-21 at 10.02.41 AMScreen Shot 2020-07-21 at 10.03.06 AM.png

Translation: We are going to graph the line f(x)=x+1 for the domain where x > 0

To make sure all our x-values are greater than or equal to zero, we create a table plugging in x-values greater than or equal to zero into the first part of our function, x+1.  Then plot the coordinate points x and y on our graph.

Screen Shot 2020-07-21 at 10.04.33 AM

Screen Shot 2020-07-21 at 10.05.00 AM.png

 

Screen Shot 2020-07-21 at 10.06.46 AM

Translation: We are going to graph the line  f(x)=x-3 for the domain where x < 0

To make sure all our x-values are less than zero, let’s create a table plugging in negative x-values values leading up to zero into the second part of our function, x-3.  Then plot the coordinate points x and y on our graph.

Screen Shot 2020-07-21 at 10.07.33 AM.png

Screen Shot 2020-07-21 at 10.07.57 AM

Ready to try the practice problems below on your own!?

Practice Questions: Graph each piecewise function:

Screen Shot 2020-07-21 at 10.08.32 AM.png

 

 

 

 

 

 

 

 

Solutions:

Screen Shot 2020-07-21 at 10.09.20 AM

Screen Shot 2020-07-21 at 10.09.58 AM.png

Still got questions?  No problem! Check out the video above or comment below for any questions. Happy calculating! 🙂

Facebook ~ Twitter ~ TikTok ~ Youtube

***Bonus! Want to test yourself with a similar NYS Regents question on piecewise functions?  Click here.

 

 

Algebra: Absolute Value Equations

Happy Wednesday math friends! Today, we’re going to go over how to solve absolute value equations.  Solving for absolute value equations supplies us with the magic of two potential answers since absolute value is measured by the distance from zero.  And if this sounds confusing, fear not, because everything is explained below!

Also, if you have any questions about anything here, don’t hesitate to comment. Happy calculating! 🙂

Absolute Value measures the “absolute value” or absolute distance from zero.  For example, the absolute value of 4 is 4 and the absolute value of -4 is also 4.  Take a look at the number line below for a clearer picture:

Screen Shot 2020-07-08 at 2.02.40 PM.png

Now let’s see how we can apply our knowledge of absolute value equations when there is a missing variable!Screen Shot 2020-07-08 at 2.03.07 PMScreen Shot 2020-07-08 at 2.03.46 PM.pngScreen Shot 2020-07-08 at 2.04.00 PMScreen Shot 2020-07-08 at 2.04.26 PM.pngScreen Shot 2020-07-08 at 2.04.56 PM

Screen Shot 2020-07-08 at 2.05.17 PM.png

Screen Shot 2020-07-08 at 2.05.39 PMNow let’s look at a slightly different example:

Screen Shot 2020-07-11 at 4.49.57 PM.pngScreen Shot 2020-07-08 at 2.07.59 PM

Screen Shot 2020-07-08 at 2.07.41 PM.png

Screen Shot 2020-07-08 at 2.08.26 PM.png

Screen Shot 2020-07-08 at 2.08.46 PM

Screen Shot 2020-07-08 at 2.09.33 PMScreen Shot 2020-07-08 at 2.09.58 PM.png Screen Shot 2020-07-08 at 2.10.39 PM.pngScreen Shot 2020-07-08 at 2.10.50 PM

Practice Questions: Given the following right triangles, find the missing lengths and side angles rounding to the nearest whole number.

Screen Shot 2020-07-16 at 9.01.08 AM.png

 

 

 

 

 

Solutions:

Screen Shot 2020-07-08 at 2.12.04 PM

Still got questions?  No problem! Check out the video the same examples outlined above. Happy calculating! 🙂

Facebook ~ Twitter ~ TikTok ~ Youtube

Algebra: How to Graph y=mx+b

Hi everyone, welcome back to Mathsux! This week we’ll be reviewing how to graph an equation of a line in y=mx+b form. And if you have not checked out the video below, please do! Happy calculating! 🙂

 

Graphing an Equation of Line: An equation of a line can be represented by the formula:Screen Shot 2020-06-17 at 9.07.16 PM

Y-Intercept: This is represented by b, the stand-alone number in y=mx+b. This represents where the line hits the y-axis.  This is always the first point you want to start with when graphing at coordinate point (0,b).

Slope: This is represented by m, the number next to x in y=mx+b. Slope tells us how much we go up or down the y-axis and left or right on the x- axis in fraction form:

Screen Shot 2020-06-17 at 9.09.42 PM

Now let’s check out an Example!

Graph the equation of a line Screen Shot 2020-06-17 at 9.10.42 PM.

Screen Shot 2020-06-17 at 9.12.01 PM

Screen Shot 2020-06-17 at 9.12.35 PM

Screen Shot 2020-06-17 at 9.13.34 PM

Screen Shot 2020-06-17 at 9.14.20 PMTry the following practice questions on your own!

Practice Questions:

Screen Shot 2020-06-17 at 9.15.22 PM

Screen Shot 2020-06-17 at 9.16.21 PM

Want more Mathsux?  Don’t forget to check out our Youtube channel and more below! And if you have any questions, please don’t hesitate to comment below. Happy Calculating! 🙂

Facebook ~ Twitter ~ TikTok ~ Youtube

 

 

Algebra: 4 Ways to Factor Quadratic Equations

*If you haven’t done so, check out the video that goes over this exact problem, and don’t forget to subscribe!

Screen Shot 2020-06-02 at 3.03.55 PMScreen Shot 2020-06-02 at 3.04.24 PM____________________________________________________________________Screen Shot 2020-06-02 at 3.20.04 PM____________________________________________________________________

Screen Shot 2020-06-02 at 3.07.02 PM____________________________________________________________________
Screen Shot 2020-06-02 at 3.07.42 PM
Choose the factoring method that works best for you and try the practice problems on your own below!

Practice Questions:

Screen Shot 2020-06-02 at 3.09.58 PMSolutions:

Screen Shot 2020-06-02 at 3.10.30 PM

Want a review of all the different factoring methods out there?  Check out the ones left out here (DOTS and GCF) and happy calculating! 🙂

Facebook ~ Twitter ~ TikTok ~ Youtube

Algebra: Completing the Square

Learn how to Complete the Square by clicking on the Youtube video and trying the practice problems below. Happy Calculating! 🙂

Click the picture below to view the Youtube video.

Complete the Square copy

Screen Shot 2020-05-23 at 5.28.18 PMPractice Questions:

Screen Shot 2020-05-23 at 5.28.54 PM

Solutions:

Screen Shot 2020-05-23 at 5.29.19 PM

Need more of an explanation?  Check out why we complete the square in the first place here and please don’t forget to subscribe! 🙂

COVID-19: What does #FlattenTheCurve even mean?

If you are a human on Earth, then I’m sure you’ve heard about the coronavirus and are currently social distancing. Here in NYC, I’m quarantining like everyone else and listening to all the beautiful math language that has suddenly become mainstream (so, exciting)!  #FlattenTheCurve has become NY’s new catchphrase and for anyone confused about what that means, you’ve come to the right place!

The coronavirus spreads at an Exponential Rate, which means it spreads in a way that increases faster and faster every day.

What does this mean?

For Example, one person with the virus can easily spread the virus to 5 other people, those 5 people can then spread the virus to another 5 people each for a total of an extra 25 people, these 25 people can then spread it to another 5 people each for an extra 125 infected people! And the pattern continues……. See below to get a clearer picture:

Screen Shot 2020-04-12 at 1.26.39 PMScreen Shot 2020-04-12 at 1.20.22 PM.   *Note: These numbers are not based on actual coronavirus data

The Example we just went over is equal to the exponential equation Screen Shot 2020-04-12 at 1.21.48 PM, but it is only that, an Example! The exact pattern and exponential equation of the future progress of the virus is unknown! We mathematicians, can only measure what has already occurred and prepare/model for the future.  To make the virus spread less rapidly, it is our duty to stay home to slow the rate of this exponentially spreading virus as much as possible.

We want to #FlattenTheCurve a.k.a flatten the increasing exponential curve of new coronavirus cases that appear every day! Hopefully, this post brings some clarity to what’s going on in the world right now.  Even with mathematics, the true outcome of the virus may be unknown, but understanding why we are all at home in the first place and the positive impact it has is also important (and kind of cool).

Stay safe math friends and happy mathing! 🙂

Also, please don’t forget to follow more Mathsux on Twitter and Facebook!

~Twitter ~ Facebook~

 

Bored and Confused?

Calling all students, teachers, and parents!  As everyone is stuck at home during a global pandemic, now is a great time we are all forced to try and understand math (and our sanity level) a little bit more.  Well, I may not be able to help you with the keeping sanity stuff, but as far as math goes, hopefully, the below websites offer some much needed mathematic support.

All jokes aside I hope everyone is staying safe and successfully social distancing.  Stay well, math friends! 🙂

Kahn Academy: The same Kahn Academy we know and love still has amazing videos and tutorials as usual, but now they also have a live “homeroom” chat on Facebook LIVE every day at 12:00pm. The chats occur daily with Kahn Academy founder Sal and at times feature famous guests such as Bill Gates. Click the link below for more:

Khan Academy Homeroom Screen Shot 2020-04-04 at 12.21.20 PM

 

Study.com: In a time when companies are being more generous, Study.com is here for us as they offer up to 1000 licenses for school districts and free lessons for teachers, students, and parents.  Check out all the education freebies here:

Study.com

Screen Shot 2020-04-04 at 1.26.03 PM

 

Math PlanetIf you’re looking for free math resources in Pre-Algebra, Algebra, Algebra 2, and Geometry then you will find the answers you need at Math Planet.  All free all the time, find their website here:

MathPlanet 

Screen Shot 2020-04-04 at 1.38.22 PM

JMAP: For anyone who has to take the NYS Regents at some point (whenever we’re allowed to go outside again), JMAP has every old Regents exam as well as answers to boot! Did I mention each exam is free and printable?  Find their website here:

JMAP

Screen Shot 2020-04-04 at 1.46.47 PM

What is your favorite educational site?  Let me know in the comments, and stay well! 🙂

Algebra: Rate of Change

Screen Shot 2018-12-28 at 8.21.26 AMScreen Shot 2018-12-28 at 8.22.23 AMScreen Shot 2018-12-28 at 8.23.21 AMScreen Shot 2018-12-28 at 8.24.00 AMScreen Shot 2018-12-28 at 8.24.30 AM.pngScreen Shot 2018-12-28 at 8.25.03 AM.png

Extra Tip! Notice that we added the labels feet/second to our answer.  Why does this make sense?? The question tells us that P(t) represents feet and that t is equal to seconds.  Another way to look at this question when applying it to the slope formula is to realize that we are finding the change of feet divided by the change of seconds.                                                          ____________________________________________________________________________________

Still got questions?  Let me know in the comments and as always happy calculating!:)

Keep in touch with MathSux at these great sites!

~Facebook~Twitter~

Summertime Review: Factoring

Screen Shot 2018-08-28 at 9.14.35 PM.png

Screen Shot 2018-08-18 at 7.28.23 PMScreen Shot 2018-08-18 at 7.28.55 PM.pngScreen Shot 2018-08-18 at 7.29.04 PM.pngScreen Shot 2018-08-18 at 7.29.37 PM.pngScreen Shot 2018-08-18 at 7.30.25 PM.pngScreen Shot 2018-08-18 at 7.30.55 PM.pngScreen Shot 2018-08-18 at 7.39.01 PM.pngScreen Shot 2018-08-18 at 7.39.42 PM.pngScreen Shot 2018-08-18 at 7.40.11 PM.png

Screen Shot 2018-08-18 at 7.42.22 PM.pngScreen Shot 2018-08-18 at 7.42.27 PM.png

Screen Shot 2018-08-18 at 7.43.17 PM.png

Screen Shot 2018-08-18 at 7.43.48 PM.png

Screen Shot 2018-08-18 at 7.44.21 PM.png

Screen Shot 2018-08-18 at 7.44.56 PM.pngScreen Shot 2018-08-18 at 7.45.54 PM.pngScreen Shot 2018-08-18 at 7.47.25 PM.png

Screen Shot 2018-08-18 at 7.47.49 PM.png

Screen Shot 2018-08-18 at 7.48.33 PM.png

Screen Shot 2018-08-28 at 9.17.31 PM.png

Screen Shot 2018-08-28 at 9.17.57 PM.png

Whether you are ready to go back to school or back to sleep, I hope you found this factoring review helpful.

Still got questions?  Don’t hesitate to reach out in the comments below! Happy math-ing! 🙂

And if you’re looking for more math-sux don’t forget to follow us out on Twitter and Facebook!

Simultaneous Equations/New YouTube Channel!

In need of a bit of review on Simultaneous Equations?  Well, now is your chance! Learn how to solve these confusing bad mama jamma’s in three different ways and choose which one works best for you!

I’m also excited to introduce my new YouTube page for MathSux!  Hope these new set of videos help.  Let me know if you have any more questions in the comments.  Happy calculating! 🙂

Need more MathSux in your life?  Follow us on these great sites!

~ Facebook ~ Twitter ~ YouTube ~

Screen Shot 2018-01-11 at 11.28.32 AM.png