Functions 2.4 Simplifying Rational Functions

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  • เผยแพร่เมื่อ 15 ธ.ค. 2024

ความคิดเห็น • 24

  • @billnyeyomomaguy7458
    @billnyeyomomaguy7458 ปีที่แล้ว +7

    Hi Ms Havrot,
    I am currently in Grade 11 Functions and will be starting Unit 2 Lesson 2.5 tomorrow in class.
    I just wanted to comment that your videos have helped me so much since the start of MCR3U for me. I struggled in mathematics during grade 9 & 10, I did not do any lessons, homework etc and it caused a major setback.
    After watching your videos I have learned so much and truly appreciate what you do and I hope you can keep up the great work.
    Thank you for spreading your knowledge.

    • @mshavrotscanadianuniversit6234
      @mshavrotscanadianuniversit6234  ปีที่แล้ว +5

      So nice of you to send me this warm message. I love hearing about how I am making a difference. I wish you the best in Functions and hope that you continue to watch next year as well. 😊

  • @hampter5274
    @hampter5274 2 ปีที่แล้ว +11

    your videos are carrying me through highschool math, thank you so much!!

    • @mshavrotscanadianuniversit6234
      @mshavrotscanadianuniversit6234  2 ปีที่แล้ว

      Happy to help! Hope you find everything you need here. If you have any questions feel free to ask. : )

  • @jaymarsh321
    @jaymarsh321 6 ปีที่แล้ว +5

    Very clear explanation than you for going through all the examples.

    • @mshavrotscanadianuniversit6234
      @mshavrotscanadianuniversit6234  6 ปีที่แล้ว

      Thank you Jay. If there is anything you would like me to explain please leave me a message Good luck with your studies!

  • @ConnorDela
    @ConnorDela 3 ปีที่แล้ว +1

    14:23, if this were a test ;) would you leave the brackets or distribute the negative?
    Generally, would you expand everything for final answers? Or is that preference?

    • @mshavrot_math
      @mshavrot_math 3 ปีที่แล้ว +3

      I would leave it in factored form. Basically, in factored form, it is easiest to see what the zeros are for the function if you are asked to graph the function.

  • @toriyt3976
    @toriyt3976 2 ปีที่แล้ว

    On 4:05 why is it not x not equal to -3 and +2? Do we switch the signs?

    • @mshavrotscanadianuniversit6234
      @mshavrotscanadianuniversit6234  2 ปีที่แล้ว

      You need to remember that you want to know what makes the denominator equal to zero and that is what you do NOT want x to be equal to.
      So, if you forget, you can always set each of the bracketed terms equal to zero and solve and you will find what x can NOT be equal to or else the function would be undefined at those points as you can not have a zero in the denominator.

  • @spookays
    @spookays 2 ปีที่แล้ว

    Hello Ms Havrot!
    I was curious on why **x** was not equal to one in the question "Simplify and State the domain" 14:45

    • @mshavrot_math
      @mshavrot_math 2 ปีที่แล้ว

      It cannot be equal to one because if you sub one into the equation you would get a zero in the denominator 😊

    • @mshavrotscanadianuniversit6234
      @mshavrotscanadianuniversit6234  2 ปีที่แล้ว +1

      Basically restrictions are what would make the denominator equal to zero

    • @spookays
      @spookays 2 ปีที่แล้ว

      Ah, thank you so much!

  • @wedelaney9669
    @wedelaney9669 2 ปีที่แล้ว

    hi miss,
    I was just wondering why at 14:19 the numerator became negative when you divided (x-1) and (1-x) out of the equation

    • @mshavrotscanadianuniversit6234
      @mshavrotscanadianuniversit6234  2 ปีที่แล้ว

      X- 1 divided by 1 - X
      Remember that 1 - x = - x + 1
      = -( x - 1)
      So now you would have (x-1) / -(x-1) which is -1
      Another way you can think of it is if you let x =3
      You would have 3-1/ 1-3 = 2/-2 = -1 which proves that the answer is -1
      Hope that helps! 😊

  • @aishamohamed2296
    @aishamohamed2296 6 ปีที่แล้ว

    Can you explain what you did in question 2? When you were crossing the (x-1) and (1-x)

    • @mshavrotscanadianuniversit6234
      @mshavrotscanadianuniversit6234  6 ปีที่แล้ว +2

      Listen to my response a second time ... The other option is to see it this way: Factor out a negative one from ( 1 - x ) and you would get - (-1 + x) right? and ( -1 + x) is the same as (x - 1) just as if I said -1 + 2 = 2 - 1 .... SO that means that once you factor out a negative the two brackets are the same, so now when you divide them out the -1 is still there. Therefore they divide into each other - 1 times. Does that help?

  • @juliamarquez6264
    @juliamarquez6264 2 ปีที่แล้ว

    Hi miss, I have a test on Chapter 2 tomorrow and I'm still having some trouble identifying the restrictions and domain. I'm not really sure on what to do without looking at the textbook solutions.

  • @beckstar78
    @beckstar78 3 ปีที่แล้ว +1

    why isn't zero always a restriction

    • @mshavrotscanadianuniversit6234
      @mshavrotscanadianuniversit6234  3 ปีที่แล้ว +2

      Well, say for example we had (x+3) in the denominator. 0 would not be a restriction because if I set x=0 the denominator would be 3 and I CAN divide by 3. However, if x = -3 then we have a problem (and a restriction) because when I set x= -3 my denominator would be 0 and I can not divide by zero. So basically if you set the denominator equal to zero and solve for x that will be your restriction. 😊

    • @beckstar78
      @beckstar78 3 ปีที่แล้ว +1

      @@mshavrotscanadianuniversit6234 thanks! i kinda caught on after i asked lol