How Do Two Graphs Differ?

Discussion in 'Algebra' started by harpazo, Apr 24, 2024.

  1. harpazo

    harpazo

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    Suppose that the graph of a function f is known. Explain how the graph of y = 4•f(x) differs from the graph of y = f(4x).


    Let me see.

    For the graph of y = 4•f(x), we stretch the graph vertically because 4 > 1.

    For the graph of y = f(4x), we compress the graph horizontally because 4 > 1.

    You say?
     
    harpazo, Apr 24, 2024
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  2. harpazo

    Vaquita3

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    Yes. "Vertically" with respect for the y-axis and "horizontally" with respect for the x-axis.
    I had a teacher that was cruelly particular about this. Would regularly switch the axes on tests to make sure we were paying attention to the orientation of the graphs themselves. It hurt. I never forgot. Is this academic trauma response?
     
    Vaquita3, Apr 26, 2024
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    harpazo likes this.
  3. harpazo

    harpazo

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    Academic trauma response?
     
    harpazo, Apr 26, 2024
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  4. harpazo

    Vaquita3

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    Yeh. A response ingrained deep into the psyche and originating in an experience from within the world of academia.
     
    Vaquita3, Apr 29, 2024
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  5. harpazo

    harpazo

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    Let's stay focused on mathematics. I am not interested in deep psychological discussions or philosophy.
     
    harpazo, Apr 30, 2024
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  6. harpazo

    conway

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    Vaquita3 was only trying to be friendly and make a joke about their days in college. I was trying to discuss philosophy. Please forgive me, I accept you are not interested in philosophy, or how it merges with mathematics. Good Luck in your studies!
     
    conway, Apr 30, 2024
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  7. harpazo

    harpazo

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    I am not offended. At 59, however, I don't have time for jokes and philosophy, well, that's another course.
     
    harpazo, May 1, 2024
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  8. harpazo

    RobertSmart

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    Your explanation is spot on!

    When we have y = 4•f(x), the graph is stretched vertically by a factor of 4, since multiplying the function by 4 stretches it vertically.

    On the other hand, with y = f(4x), the graph is compressed horizontally by a factor of 1/4. This is because replacing x with 4x inside the function causes it to compress horizontally.

    Your understanding highlights the essential differences in how these two transformations affect the graph. Great job!

    And sure, if you need further assistance with math assignments or any other academic help, you might find mathassignmenthelp.com useful. They offer support for various mathematical topics and could be a valuable resource for your assignments. You can also contact them by dialing +1 (315) 557-6473.
     
    RobertSmart, May 1, 2024
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  9. harpazo

    harpazo

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    I am strictly interested in mathematics.
     
    harpazo, May 26, 2024 at 9:05 AM
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  10. harpazo

    harpazo

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    I am interested in discussing math here. Look for my questions.
     
    harpazo, May 26, 2024 at 9:06 AM
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