Let f(x)=−3x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.What is the equation for g(x) ?Enter your answer in the box.g(x)= ___________The graph of the function f(x)=|3x| is translated 4 units up.What is the equation of the transformed function?Enter your answer in the box.g(x)= ___________
Accepted Solution
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Answer:Ques 1) [tex]g(x)=-12x+48[/tex]Ques 2) [tex]g(x)=|3x|+4[/tex]Step-by-step explanation:Ques 1)We know that if a graph is stretched by a factor of a then the transformation if given by: f(x) → a f(x)Also, we know that the translation of a function k units to the right or to the left is given by: f(x) → f(x+k)where if k>0 then the shift is k units to the leftand if k<0 then the shift is k units to the right.Here the graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.This means that the function g(x) is given by:[tex]g(x)=4f(x-4)\\\\i.e.\\\\g(x)=4(-3(x-4))\\\\i.e.\\\\g(x)=-12(x-4)\\\\i.e.\\\\g(x)=-12x+48[/tex]Ques 2)We know that the transformation of the type: f(x) → f(x)+kis a shift or translation of the function k units up or down depending on k.If k>0 then the shift is k units up.and if k<0 then the shift is k units down.Here, The graph of the function f(x)=|3x| is translated 4 units up.
This means that the transformed function g(x) is given by: [tex]g(x)=|3x|+4[/tex]