@Fizaaahhh Great question! You're right, 3 > 3 is an invalid statement. However, the reason we plug in 3 to evaluate the point is just so the graphs lines up properly. If you want, you could plug in something really close to 3 like 3.0000001, but you're basically going to get the same answer which is why it's easier if we just use 3 to evaluate it. Also, when graphing our line on the corrdinate plane, we make sure we put an OPEN circle because thats how we show the graph doesnt actually touch or include x = exactly 3, but that it does include all numbers greater than 3. Hope that helps 👍
Hands down the BEST explaination video I've found for these graphs so far! Clear, concise and to the point. Thank you so much! You literally just saved me from failing my Maths final.❤
I’m learning piecewise functions in my Algebra 2 class and i told my teacher i could not figure out how to find the domain and range but you perfectly described it and now i feel more confident about finding the domain and range
Thank you so so much. All the videos from my usual sources only used function rules like this examples middle one. I had no idea what I was doing for ones like x
You're welcome! I try to mix up as many examples as possible, but if there's ever something specific you're looking for, just let me know and I can answer you here in the comment section or even make a video for it 👍
Would I still use the table method if the function had a squared in it? for ex: f(x) ={ (x-4)^(2) + 1; x > 2 or f(x) ={ x^(2) + 1; x > 0 note: ^(2) means the squared sign
Great question! Yes you could still use a table to graph your functions. The only difference is you'd want to use at least 3 points instead of 2 since you have quadratic equations (aka parabolas) and I graphed linear equations (aka straight lines) in this video. The function f(x)=(x-4)^(2) + 1 is in vertex form so we can see that the vertex is at (4,1) The limit of the function is x > 2, so we want to plug in x-values that are bigger than 2. We can use x = 2,4, and 6. Why would we want to use 2? Because that's the limit of your function (x>2) Why use 4? Because that's where the vertex is. Why use 6? Because it's 2 spots away from the vertex, just like x=2 is 2 spots away from the vertex. For f(x)=x^2 + 1, it's kind of in vertex form too so we can see the vertex would be at (0,1). The limit of the function is x > 0, so we want the values we plug in to be greater than zero. We can use x= 0,1, and 2. Why use 0? It's the limit of the function. Why use 1? It's bigger than zero and an easy number to evaluate. Why use 2? It's also bigger than zero and an easy number to evaluate. For some clarification on vertex form you can watch this video: ruclips.net/video/_8cISMjZuj0/видео.htmlsi=W3nCnq1wHCIH9BFx Otherwise I hope that helped but let me know if you still have any questions, good luck! 👍
Great question! You're right, 3 > 3 is an invalid statement. However, the reason we plug in 3 to evaluate the point is just so the graphs lines up properly. If you want, you could plug in something really close to 3 like 3.0000001, but you're basically going to get the same answer which is why it's easier if we just use 3 to evaluate it. Also, when graphing our line on the coordinate plane, we make sure we put an OPEN circle because thats how we show the graph doesnt actually touch or include x = exactly 3, but that it does include all numbers greater than 3. Hope that helps 👍
Watched this video four days ago but I struggle with when to write the range as single and when to write them separately for each function do they have to share a point in each x and y axis together in order to write it as a single range?
Great question! Piecewise functions will always share x coordinates because where one function ends, the next one begins. I'm not sure you have to write the range for each function (unless you're specifically asked to). Generally, writing a single range that covers the whole graph should be good enough 👍
@@Eat_Pi ohh thanks, but sorry I forgot to mention by saying ( writing each range separately) I meant when you use the union method to just combine the ranges that u separately wrote for each function, like I have seen questions they do that and they sometimes write the range as a single one like the one u did in the video for both ( not combining the ranges of each function with the union thingy) so I’m kinda confused on when to use each one.
@@sunflowerflower2796 Oh I see! Well if there's a gap in the range then you should definitely split them up, but if all the functions are connected/overlap (like they do the example I covered in this video) then you should be able to write just a single range for the whole thing. It'd be a good idea to ask your teacher too if they have a preference, but if they don't, then that's how I would determine if I need to write more than 1 range: simply if there's a gap. Hope that clears it up a little! 👍
Hi there! Yes the difference is: domain = x-value limits range = y-value limits Domain: In this example the graph points to the left in the negative x-direction, and points to the bottom right in the positive x-direction. So it covers all x-values so we can say the domain is All Real Numbers or we can write it in interval notation as (-∞,∞) Range: There's no arrows pointing up. The highest part of the whole graph is in the middle where y = 2. Notice there's a closed circle at the highest part (so that means we use a bracket to include this point). The graph on the right side is pointing down and to the right in the negative y-direction. So the highest y-value is 2 and it goes down to negative infinity so we can write it in interval notation as [2,-∞) Hope that helps! 👍
Let me know if you have any questions! it's good to practice the same problem a few times to make sure you understand the process. Otherwise its time to start filling out some job applications 🙏
Good question! It's because the biggest y-value is positive 2 and the rest of the y-values are beneath that high point. So all the y-values are smaller than 2, or in other words, *less than* 2 👍
you should've explained the last part better. If you have to choose something greater than 3, and you chose 3 as well then what's the point of closed and open circle? You should've clarified that instead of going along with 3 and then 4 and explained why you chose them
@TheOwlTheOne Thanks for the feedback! You're right, 3 > 3 is an invalid statement. However, the reason we plug in 3 to evaluate the point is just so the graphs lines up properly. If you want, you could plug in something really close to 3 like 3.0000001, but you're basically going to get the same answer which is why it's easier if we just use 3 to evaluate it. Also, when graphing our line on the corrdinate plane, we make sure we put an OPEN circle because thats how we show the graph doesnt actually touch or include x = exactly 3, but that it does include all numbers greater than 3. Hope that helps 👍
The range is the limit of the y values, so on this graph we have y-values from positive 2, down to negative infinity. You could write that as: y ≤ 2 or [2, -∞) Both would be valid answers 👍
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If x>3, how can we substitute the value 3 along with 4 when its already given x is bigger than 3, its only possible id x> or equal to 3 right? 3:44
@Fizaaahhh Great question!
You're right, 3 > 3 is an invalid statement. However, the reason we plug in 3 to evaluate the point is just so the graphs lines up properly. If you want, you could plug in something really close to 3 like 3.0000001, but you're basically going to get the same answer which is why it's easier if we just use 3 to evaluate it.
Also, when graphing our line on the corrdinate plane, we make sure we put an OPEN circle because thats how we show the graph doesnt actually touch or include x = exactly 3, but that it does include all numbers greater than 3.
Hope that helps 👍
I LITERALLY CRIED BECAUSE IT FINALLY MADE SENSE
I found you crying 😭
I crew too 😭
We both crode 😭
That’s actually real bro
@@AngelinaPerez-Duque I LOVE TO MAKE EVERYONE CRY!
(preferably happy tears but either way I guess)🤷
sameeee
@@AngelinaPerez-Duque BAHHAHA
this is the only video that made me understand piecewise function, tysm!!
I'm so glad to hear it made sense! And you're welcome 😃
You explained this topic better than my gen math teacher
lol well I'm glad it made sense! 😃
HAHA trueeelalets
Hands down the BEST explaination video I've found for these graphs so far! Clear, concise and to the point. Thank you so much! You literally just saved me from failing my Maths final.❤
Thank you for the kind words, I'm so glad you found the video helpful! And goodluck on your final - crush it like a friggin genius! 😎
@@Eat_Pi Just wanted to remind you that I scored an A++ because of you! Thank you sooo much once again! You're an angel. ❤️❤️
@tayluvofficial Great job!! That's incredible to hear, I'm so proud of you! 😃
And you're very welcome, I'm always happy to help! 👍
even organic chemistry tutor couldn't help me on this, thank you so much🙏🙏
He's great! Sometimes you just have to see it a different way though - but I'm glad it was helpful! 👍
Explained it the best by far! Thank you
You're very welcome - I'm glad it made sense! 👍
I’m learning piecewise functions in my Algebra 2 class and i told my teacher i could not figure out how to find the domain and range but you perfectly described it and now i feel more confident about finding the domain and range
@theyluvgrace1 Yeah this is definitely a tricky subject at first, but I'm so happy to hear it makes sense now! 🙏
From all the videos I’ve watched, you’ve explained it perfectly. Thank you so much! This is really helpful.
You're welcome, that means a lot to hear! I'm so glad it made sense :D
I was really confused when it came to piecewise functions but you made it all make sense ,ty!!
You're welcome! I'm always trying to make things as clear as possible 👍
thank you so much you helped me the day before my math test
@@sanihadogganahalli2719 You're welcome! Crush that test tomorrow like a friggin genius 😎
You deserve a sub man I watched this before my pre calculus exam and it helped allot I shared it with my friends so they could benefit as well
That's incredibly nice of you, thank you! I hope it helped all of you ACE your exam like the friggin geniuses that you are! 🙏
@@Eat_Pi THANK YOU MISTA GENIUSSSS
@@Myroku7 💪🧠
Thank you man, I have a test today first period
Hope you crushed that test today like a friggin genius 😎
Thank you so so much. All the videos from my usual sources only used function rules like this examples middle one. I had no idea what I was doing for ones like x
You're welcome! I try to mix up as many examples as possible, but if there's ever something specific you're looking for, just let me know and I can answer you here in the comment section or even make a video for it 👍
This was great! Helped me relearn functions to help my kid out with her math homework.
That's awesome, I'm so glad to hear that! 😃
This video helped me solve my problem. Thank you! ❤
That's great to hear, and you're welcome! :D
Thank You so much for your help! I have my first quiz for 9th grade alg 2 honors tmrw and you saved me!
@VedhGajawada-jt3ri I'm so happy to hear it was helpful! Now go crush that quiz like a friggin genius 😎
i have my first calc quiz tomorrow THANK YOU SO MUCH IT FINALLY MAKES SENSE 😭😭
@izabelsdemis3 I love those lightbulb moments! 😄
I'm happy it helped and good luck on that calc quiz, crush it like a friggin genius! 😎
Omg you made it so easy to understand. Thank you so much ❤❤❤
@evelins6563 That's great to hear! I'm glad it made sense, and you're welcome :D
I need this dude as my teacher fr mine sucks at explaining lol
@@Chris-gp2ql I'm always around if you have any questions 😎
Thank you , it's easier than the other I've watched.
You're welcome! I'm really glad to hear it was helpful! 👍
Hiii, just wondering what the interval notation for the question is, thank u!
Great question! I should've written it down lol
Domain: (-∞,∞)
Range: (-∞,2]
amazing explanation!
Glad you think so! 🙏
Nice one 👍👍
I appreciate that, thank you! 😃
Great one👌!
Thank you, I'm glad it was helpful!
my math final is tomorrow so this helped
Samee😊
thanks a lot
you're welcome a lot ✌️✌️✌️✌️✌️✌️
Short and sweet 😊 just saved my CA
lol I'm glad I could save you! 😄
Would I still use the table method if the function had a squared in it? for ex: f(x) ={ (x-4)^(2) + 1; x > 2 or f(x) ={ x^(2) + 1; x > 0 note: ^(2) means the squared sign
Great question! Yes you could still use a table to graph your functions. The only difference is you'd want to use at least 3 points instead of 2 since you have quadratic equations (aka parabolas) and I graphed linear equations (aka straight lines) in this video.
The function f(x)=(x-4)^(2) + 1 is in vertex form so we can see that the vertex is at (4,1)
The limit of the function is x > 2, so we want to plug in x-values that are bigger than 2. We can use x = 2,4, and 6.
Why would we want to use 2? Because that's the limit of your function (x>2)
Why use 4? Because that's where the vertex is.
Why use 6? Because it's 2 spots away from the vertex, just like x=2 is 2 spots away from the vertex.
For f(x)=x^2 + 1, it's kind of in vertex form too so we can see the vertex would be at (0,1).
The limit of the function is x > 0, so we want the values we plug in to be greater than zero. We can use x= 0,1, and 2.
Why use 0? It's the limit of the function.
Why use 1? It's bigger than zero and an easy number to evaluate.
Why use 2? It's also bigger than zero and an easy number to evaluate.
For some clarification on vertex form you can watch this video: ruclips.net/video/_8cISMjZuj0/видео.htmlsi=W3nCnq1wHCIH9BFx
Otherwise I hope that helped but let me know if you still have any questions, good luck! 👍
this helped a bunch, thanks!
That's awesome, I'm glad it did! And you're welcome :D
Oh my goodness you’re the GOATTTTTTTTT
I'm glad it was helpful! Doin my best for all you friggin geniuses 🐐🔥😎
DUDE, you just saved me thanks
lmao I'm glad to hear it! I'm here to save any and all friggin geniuses 😅
great video
I'm glad you liked it!
This is a masterpiece
I appreciate that 🙏
@@Eat_Pi No I appreciate you for saving me from failing man
@@tridentgaming7514 LOL I'm glad you're not going to fail! And I'm always around if you need help 👍
For -2x+4 if x>3... why would we use the number 3 if it says its GREATER than, not equal to 3?
Great question!
You're right, 3 > 3 is an invalid statement. However, the reason we plug in 3 to evaluate the point is just so the graphs lines up properly. If you want, you could plug in something really close to 3 like 3.0000001, but you're basically going to get the same answer which is why it's easier if we just use 3 to evaluate it.
Also, when graphing our line on the coordinate plane, we make sure we put an OPEN circle because thats how we show the graph doesnt actually touch or include x = exactly 3, but that it does include all numbers greater than 3.
Hope that helps 👍
Watched this video four days ago but I struggle with when to write the range as single and when to write them separately for each function do they have to share a point in each x and y axis together in order to write it as a single range?
Great question! Piecewise functions will always share x coordinates because where one function ends, the next one begins. I'm not sure you have to write the range for each function (unless you're specifically asked to). Generally, writing a single range that covers the whole graph should be good enough 👍
@@Eat_Pi ohh thanks, but sorry I forgot to mention by saying ( writing each range separately) I meant when you use the union method to just combine the ranges that u separately wrote for each function, like I have seen questions they do that and they sometimes write the range as a single one like the one u did in the video for both ( not combining the ranges of each function with the union thingy) so I’m kinda confused on when to use each one.
@@sunflowerflower2796 Oh I see! Well if there's a gap in the range then you should definitely split them up, but if all the functions are connected/overlap (like they do the example I covered in this video) then you should be able to write just a single range for the whole thing.
It'd be a good idea to ask your teacher too if they have a preference, but if they don't, then that's how I would determine if I need to write more than 1 range: simply if there's a gap.
Hope that clears it up a little! 👍
@@Eat_Pi thank you so much really appreciate it 🌻
Your the goat
@lukecharske5990 Thanks bro I'm happy to help 👍
what number would i put for the x y table if x < 1
Good question! The x-values you could use for the table could be things like -1, 0, and 1 👍
What if we don't have two lines that go on forever (in this case) but only one line, what would be the domain in that case?
Good question! It would depend on which direction the line is going. I can give you a better answer if you tell me your specific problem 👍
Massive 🙏🙏🙏🙏
Happy to help! 🙏🙏🙏🙏
THANK YOU!
You're very welcome! :D
Thank you❤❤❤❤❤
You're welcome 💙💙💙💙💙
Thank you 🌻
You're very welcome! 😃
thank you so much!!!
You're welcome, I'm glad it was helpful! And go crush that final like a friggin genius 😎
Can I please get an example of determining if a piecewise relation is a function, please 🙏
Hello I got my exam next week can you explain the domain and range part tysm!
Hi there! Yes the difference is:
domain = x-value limits
range = y-value limits
Domain:
In this example the graph points to the left in the negative x-direction, and points to the bottom right in the positive x-direction. So it covers all x-values so we can say the domain is All Real Numbers or we can write it in interval notation as (-∞,∞)
Range:
There's no arrows pointing up. The highest part of the whole graph is in the middle where y = 2. Notice there's a closed circle at the highest part (so that means we use a bracket to include this point).
The graph on the right side is pointing down and to the right in the negative y-direction.
So the highest y-value is 2 and it goes down to negative infinity so we can write it in interval notation as [2,-∞)
Hope that helps! 👍
@@Eat_Pi thank you so much!
i’m cooked for my exam on tuesday 😭
Let me know if you have any questions! it's good to practice the same problem a few times to make sure you understand the process.
Otherwise its time to start filling out some job applications 🙏
Why is it less than for the range
Good question! It's because the biggest y-value is positive 2 and the rest of the y-values are beneath that high point. So all the y-values are smaller than 2, or in other words, *less than* 2 👍
@@Eat_Pi thx
@@Snail109 happy to help!
i love you.
I love me too... but I feel strongly about you as well.
Thanks my teacher is so confusing
Lol that happens sometimes but I'm glad it makes sense now! 🙏
you should've explained the last part better. If you have to choose something greater than 3, and you chose 3 as well then what's the point of closed and open circle? You should've clarified that instead of going along with 3 and then 4 and explained why you chose them
@TheOwlTheOne Thanks for the feedback!
You're right, 3 > 3 is an invalid statement. However, the reason we plug in 3 to evaluate the point is just so the graphs lines up properly. If you want, you could plug in something really close to 3 like 3.0000001, but you're basically going to get the same answer which is why it's easier if we just use 3 to evaluate it.
Also, when graphing our line on the corrdinate plane, we make sure we put an OPEN circle because thats how we show the graph doesnt actually touch or include x = exactly 3, but that it does include all numbers greater than 3.
Hope that helps 👍
❤
🧡🖤
The range of the function would be like -(1/0), 3 am I right?
The range is the limit of the y values, so on this graph we have y-values from positive 2, down to negative infinity. You could write that as:
y ≤ 2
or
[2, -∞)
Both would be valid answers 👍
this is still so confusing to me..
I'm sorry to hear that! If you give me your problem I could probably walk you through it 👍
I’m dying in ap pre calc rn thank u for this 🥲
You're welcome! I'm here to save all of you friggin geniuses 😎
Thank you❤
Happy to help 🧡