Determining if a Function is Linear, Quadratic, or Exponential from a Table

If we are given a table of functions, how do we determine if the functions are linear, quadratic, or exponential?
Edit - When going through the examples in this video, you'll hear me using the phrases "Change in y" or "Change in change of y (I also say change of y is delta y)". The terms you'll probably see in class are usually "First difference" and "Second difference." I wanted to write that as I don't think any teachers use "change in the change" unless they're explaining what "second difference" means. Maybe your teacher uses a different phrase (please post below, that'd be helpful for others!) but I wanted to update this with what you'll most likely see in class so you're not like "what in the world is change in change my teacher's never used that?!" 😂 Hope that helps! 🙌

[@Ren_6R]

I regret sleeping in classes, thank you for uploading this video

[@TopTierMath]

You're very welcome, I'm glad it helped!

[@user-pw9cm3vz7g]

Same-

[@bellebijoureinemere]

👌🏾👌🏾👌🏾👌🏾 clearly and easily explained. Thank you instructor 🙌

[@donnamaelorilla207]

The lesson in the modules I received was not clear enough to understand so I don't understand the lesson and other videos on youtube about this lesson are not that clear until I cross into this video lesson, it is easily and clearly explained. There are also laughs along with the lesson which is I like. It really helps me a lot, thank you very much❤️❤️

[@TopTierMath]

I'm so glad it was helpful, you're very welcome!

[@lykajhoevell]

I WATCHED ALOT OF VIDEOS ABOUT THIS TOPIC BUT YOU'RE THE ONLY ONE WHO EXPLAINED IT WELL!!!!👏🏻👏🏻

[@TopTierMath]

That means a lot, and I'm so glad it helped!

[@nyr4lif428]

This is so useful, even 6 years later!! Thank you so much, I rarely leave comments but you’re such a great teacher!! 🌟🙌

[@TopTierMath]

That's awesome to hear and it means a lot! (sheesh 6 years flies by, probably time to redo that video 😅)

[@JayJay-xv3lp]

OMG THANK YOU. Now I won’t fail math 👍

[@TopTierMath]

You’re very welcome, I’m glad it helped!

[@lilkhush2416]

You are very underrated you deserve more subs

[@TopTierMath]

I appreciate that, I'm going to keep putting out videos that hopefully help others 🙌

[@evolveag]

Beautiful Explanation Keep it up!

[@nuttygamer4337]

I really mean it and not saying it because other people are, but you deserve way more subscribers. Crystal clear explanation 💎

[@TopTierMath]

Thank you, I really appreciate that!

[@kingofmacaroni4049]

Thank you so much, saw my exam review sheet and needed to learn this

[@l_hat3951]

ty! was clear and helpful

[@TopTierMath]

I’m glad it helped! 🙌🏼

[@jackbalfour8659]

Thank you

[@TopTierMath]

You're very welcome!!

[@ianhaughey747]

Thank you i missed the day that we learned this and now we have a test thank you 🙏

[@TopTierMath]

You’re very welcome, I’m glad it helped! 🙌🏼

[@James12030]

you deserve so much more you are helping so many peoplle

[@TopTierMath]

Thank you so much, that means a lot!

[@rbaa8379]

Thank you for the upload

[@justinm412]

I hope it helped!

[@ThePiMan0903]

Very nice video sir! You deserve more subs!

[@kierawilson6018]

change in the change in the change xD. This video was really helpful and funny thanks. People are right this is a lot more clearer. 😁

[@justinm412]

😂 It feels like it never ends. I’m so glad it was helpful, thank you!

[@jonny3348]

thank you I found this video very helpful

[@TopTierMath]

Awesome, I'm glad it was helpful! 🙌

[@supernovic99]

This video was literally so useful!!!!! Thank you so much!!!

[@dianag7995]

so is the second ttable a quadratic?

[@TopTierMath]

Sorry for the late response, but why do you think it's quadratic? (Answering a question with a question, sorry it's the inner tutor in me 😅)

[@slowlycold4356]

TYYYYYY i have a quiz tmrw and i coudnt understand but now i do tysm

[@TopTierMath]

I hope you did well and you’re very welcome!

[@slowlycold4356]

@@TopTierMath Yes yes I DID

[@SteveSong756891]

THANKS FOR THE VIDEO! I understanded well!

[@poles1c]

this was extremely helpful, thank you so much!

[@TopTierMath]

I'm so glad it was helpful, you're very welcome!

[@cherrycola324]

You have a very soothing voice

[@TopTierMath]

Aww thank you, my goal is to not put people to sleep 😅

[@mianmasharratmurshed8790]

what happens if there are negative values and the differences become negative do i take the negative into account or do i just state the difference without adding a negative?

[@TopTierMath]

Great question! If the differences are negative, make sure to keep them negative. If you make them positive, (which seems reasonable, right?) it'll change the whole problem you're working on (and give you the wrong answer) because we need to see what the pattern is for the first and/or second difference and changing a negative to a positive will alter the pattern you get. I hope that helps!

[@thesaberoflightarchived]

Thank you, simply thank you

[@dyllianpecunia2009]

i don't get the second problem how is it linear

[@TopTierMath]

Hey Dyllian! I'm so sorry for the uber late response, but in case you were still wondering here's why: Linear just means a constant rate of change. So when we're dealing with coordinates like these problems, the following must be true if it's linear: Pick any two coordinates aka (x,y) points and find the change in y divided by change in x (that's where y2-y1/x2-x1 comes from). You'll get some fraction. You should get that same exact fraction (you may need to simplify) for ANY two coordinates that you pick and do the same to (change in y divided by change in x). If you get a different value for even one pair (again, remember to simplify the fraction if needed), then that set of coordinate points does not represent a linear function. Because we got the same fraction for all pairs of coordinates on problem 2, that represents a linear function. Let me know if that helps!

[@Noobbshyuga]

thanks

[@TopTierMath]

You're very welcome, I hope it helped!

[@My_Arse]

Thanks byw

[@TopTierMath]

You’re very welcome!

[@nezhaerickagacus2780]

Thank uu

[@TopTierMath]

You're very welcome, I hope it helped!

[@melatmekbib7592]

1.exponential

[@Melodeybae]

😢

[@VuTunes]

I’m sorry. But linear is the first difference so which means the 2nd problem was wrong

[@TopTierMath]

In the second problem, we did use the first difference 🤙🏼

[@yourtypicalloser404]

thank you so much it really helped your explanation is so good!!🤍🤍

[@TopTierMath]

I’m so glad it helped!!