Graphical Reasoning

Discussion in 'Other Pre-University Math' started by nycmathguy, Aug 3, 2021.

  1. nycmathguy

    nycmathguy

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    Section 1.8
    Question 26

    See attachment.

    I know how to graph f, g and f + g on the same xy-plane.

    Explain the following:

    Which function contributes most to the
    magnitude of the sum when 0 ≤ x ≤ 2?
    Which function contributes most to the
    magnitude of the sum when x > 6?


    20210803_033425.jpg
     
    nycmathguy, Aug 3, 2021
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  2. nycmathguy

    MathLover1

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    upload_2021-8-3_11-44-9.png

    Which function contributes most to the
    magnitude of the sum when 0 ≤ x ≤ 2?

    the orange line ( g(x)=sqrt(x)) contributes more when 0 ≤ x ≤ 2

    Which function contributes most to the
    magnitude of the sum when x > 6?

    blue line (f(x)=x/2) contributes most when x > 6
     
    MathLover1, Aug 3, 2021
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  3. nycmathguy

    nycmathguy

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    Sorry but I don't get it.
     
    nycmathguy, Aug 4, 2021
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  4. nycmathguy

    MathLover1

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    green line is the sum function f + g=(1/2)x+sqrt(x)
    the magnitude of the sum are y values (distance from x-axis(

    function contributes most to the magnitude of the sum when 0 ≤ x ≤ 2 is orange line ( g(x)=sqrt(x)) because
    orange line is above blue line which means y values of g(x)=sqrt(x) are greater than y values of f(x)=(1/2)x in interval [0,2]

    and blue line (f(x)=x/2) contributes most when x > 6 because blue line is above orange line which means y values of f(x)=(1/2)x are greater than y values of g(x)=sqrt(x) in interval (6,infinity]
     
    MathLover1, Aug 4, 2021
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  5. nycmathguy

    nycmathguy

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    1. Green line is the sum of the two functions.

    2. The blue line is above the orange line for values where x is greater than 6.

    Yes?

    I will do a few more and post my work when time allows.
     
    nycmathguy, Aug 4, 2021
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  6. nycmathguy

    MathLover1

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    Yes
     
    MathLover1, Aug 5, 2021
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  7. nycmathguy

    nycmathguy

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    I will work on two more when time allows and show my work.
     
    nycmathguy, Aug 5, 2021
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