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Thanks!

 Apr 21, 2021
 #1
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a) In order to plot g(x) we translate the endpoints of f(x)  as follows :- 

       \((-4,4)\) in f(x) ⇔ \((-13,2)\) in g(x) 

       \( (0,2)\) in f(x) ⇔ \((-1,1)\) in g(x) 

       \((-1,0)\) in f(x) ⇔ \((-4,0)\) in g(x)

       \((4,-4)\) in f(x) ⇔ \((11,-2)\) in g(x)

 

   ∴ The graph of g(x) is plotted below -

 

 

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b) Each point \((a,b)\) in  f(x) becomes \((3a-1,{b \over 2})\) in g(x).

 

    Now, that implies a horizontal stretch by a factor of 3 and a horizontal shift by 1 unit left for a. 

    So, that gives us \(f({1 \over 3}.(x+1))\)

 

    As for b, the graph shrinks vertically by a factor of \(1\over 2\)

    So that gives \({1\ \over 2}f({1 \over 3}.(x+1))\)

 

    So that completes, 

     \(g(x) = {1 \over 2}f({x+1 \over 3})\)

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c) In order to get the graph \(y=g(x)\), the original graph can be stretched horizontally  by a factor of 3, then shrunk vertically by a factor of 1/2 and shifted left by 1 unit. 

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~ It's a pleasure! :) 

 Apr 30, 2021

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