Graph of 4 Lines

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

  1. nycmathguy

    nycmathguy

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    Section 1.8
    Question 72

    See attachment.

    Part (a)

    I say f(p) = Line 3.

    Part (b)

    I say g(p) = Line 4.

    Part (c)

    I know that (g ° f)(p) means g(f(p)).

    I know that f(p) = Line 3.

    So, g(f(p)) = g(Line 3).

    Part (d)

    I know that (f ° g)(p) means f(g(p)).

    I know that g(p) = Line 4.

    So, f(g(p)) = f(Line 4).

    You say?

    How would you describe the situation in parts (c) and (d)?

    20210803_042056.jpg
     
    nycmathguy, Aug 3, 2021
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  2. nycmathguy

    MathLover1

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    a)

    L2
    (0,0) and (10,5)=>slope 1/2=0.5

    y-0=(1/2)(x-0)
    y=(1/2)x -> (1/2)x is 50% of x (in this case 50% discount)

    so L2 is f(p)=(1/2)p


    b) L1
    (5,0) and (10,5)=>slope 1 and x intercept 5
    y-y1=m(x-x1)
    y-0=1(x-5)
    y=x-5=> -5 represents $5 discount so this is function g(p)
    g(p)=p-5
    so, L1 is g(p)=p-5

    c)
    (g o f) (p)=g(f(p))
    (g o f) (p)=g((1/2)p)
    (g o f) (p)=(1/2)p-5 => L4

    d)
    (f o g) (p)=f(g(p))
    (f o g) (p)=f(p-5)
    (f o g) (p)=(1/2)(p-5)
    (f o g) (p)=(1/2)p-5/2 => L3
     
    Last edited: Aug 3, 2021
    MathLover1, Aug 3, 2021
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  3. nycmathguy

    nycmathguy

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    I messed up the entire set of questions.
     
    nycmathguy, Aug 4, 2021
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