Graphing Transformations | Function Dilation - Stretch and Compression

www.greenemath.com/
/ mathematicsbyjgreene
In this lesson, we will learn about graphing the function transformation known as function dilation or simply stretching or shrinking of a graph. We will explore what happens when a function g(x) is defined by multiplying a parent function f(x) by some positive real number a. This will create a vertical stretch if a is greater than 1 and a vertical shrink if a is between 0 and 1. Additionally, we will explore horizontal compressions and stretches. These occur when a function such as g(x) is defined by plugging in ax in for x in the function f(x), so essentially this becomes g(x) = f(ax). Here if a is larger than 1, we have a horizontal compression and if a is between 0 and 1, we will have a horizontal stretch.

Пікірлер: 18

  • @jenniferratto9232
    @jenniferratto92326 ай бұрын

    The best video on KZread that explains Dilation so well. Amazing job. Subscribed. Please make videos on the units of AP Calculus AB and BC. Thank you so much💕💕💕

  • @Greenemath

    @Greenemath

    6 ай бұрын

    You are welcome.

  • @GravitySix-G6
    @GravitySix-G68 ай бұрын

    the way I like to think about the horizontal stretch or shrink is that if I am already given an output or y value by a graph or table chart then I need to perform the opposite with the input or x value to keep the y value the same. But if I am graphing a new value then the value I plug in for x is the x value itself so I need to multiply by whole number or fraction whichever is given to me

  • @Greenemath

    @Greenemath

    8 ай бұрын

    Work lots of the examples in your book and think about what's happening very carefully.

  • @HastiinTliziYazhi
    @HastiinTliziYazhi3 ай бұрын

    Do you mind if we ask questions about the reading? If that is all right, I had question about example problem 3 from the complementary text. In it, f(x) = 2 - x^3. Meanwhile, g(x) = 2 - (1/8)x^3. The text then states "Since g(x) = f[(1/2)x], we can say that compared to the graph of f, g has been horizontally stretched by a factor of 2." My original thought was that g(x) was a horizontal stretch of 8. My apologies if I am missing something obvious.

  • @Greenemath

    @Greenemath

    3 ай бұрын

    For horizontal transformations, just think about how you can undo what is done to x to get the same y-value. Let's take the point (-2, 10) on the graph of f(x). How can I get that same y-value now on g(x)? f(-2) = 10 g(-4) = 10 What you want to do is plug in and go slow for each one, then it will make sense what is going on. Write them both on the same page. Then look at the graph. www.desmos.com/calculator/qemzivvgtw

  • @HastiinTliziYazhi

    @HastiinTliziYazhi

    3 ай бұрын

    @@Greenemath Thank you, now I understand. That makes it very clear that you need to do more than just glance at the coefficient of x to know the horizontal dilation.

  • @GravitySix-G6
    @GravitySix-G68 ай бұрын

    awesome video! I feel like people fail to stress the reason why vertical and horizontal are getting stretched or shrunk because of the x-axis and y-axis, respectively. Thank you for pointing out the reason because that makes sense logically and without that, it is weird to think about it. Just asking for a future plan do you have calculus 1-3 playlists? if not, any plans? That will be super helpful

  • @Greenemath

    @Greenemath

    8 ай бұрын

    I'll start working on Calculus I next year when Pre-Calculus is completed.

  • @GravitySix-G6

    @GravitySix-G6

    8 ай бұрын

    @@Greenemath ​​⁠Sounds great I can’t wait Teacher Greene! And I have a question I am wondering, how long it takes to complete full course?

  • @Greenemath

    @Greenemath

    8 ай бұрын

    @GravitySix-G6 To do all of the written lessons, graphs, practice tests, quizzes, and video lessons, maybe 5 years or so. It really depends on how fast A.I. develops.

  • @GravitySix-G6

    @GravitySix-G6

    8 ай бұрын

    @@Greenemath ​​⁠that’s incredible! Behave of everyone I am very very grateful what you are doing! It really helps us. ❤️ I have another question, how long did it take to complete college algebra, trigonometry, and other completed courses?

  • @Greenemath

    @Greenemath

    8 ай бұрын

    @GravitySix-G6 College Algebra and Trigonometry took about 18 months but that's filming maybe two or three days a week, when I have time. The written lessons, practice tests, quizzes, and computer generated tests I have built take an enormous amount of time. I spend most of my free time working on that.

  • @bruhmomentoprimo
    @bruhmomentoprimo2 жыл бұрын

    super helpful tysm

  • @Greenemath

    @Greenemath

    2 жыл бұрын

    You are welcome.

  • @thiplethiple123
    @thiplethiple1239 ай бұрын

    nice video

  • @Greenemath

    @Greenemath

    9 ай бұрын

    Thanks