f(x)=x4+2x+6; vertical stretch by a factor of 2, followed by a translation 4 units right

[tex]h(x)=2(x-4)^4+4(x-4)+12[/tex]Explanation:Vertical stretch is a non-rigid transformation because it causes a distortion in the graph of the function.Translation is a rigid transformation because the basic shape of the graph is unchanged.Let:[tex]f(x) \ a \ function \ and \ g(x) \ the \ transformation \ of \ f(x): \\ \\ g(x)=cf(x) \\ \\ If \ c>1 \ is \ a \ vertical \ stretch[/tex][tex]f(x) \ a \ function \ and \ g(x) \ the \ transformation \ of \ f(x): \\ \\ g(x)=f(x-c) \\ \\ For \ c>0 \ shift \ the \ graph \ c \ units \ right[/tex]So, the transformations:Vertical stretch by a factor of 2:[tex]g(x)=2f(x) \\ \\ g(x)=2(x^4+2x+6) \\ \\ g(x)=2x^4+4x+12[/tex]Translation 4 units right:[tex]h(x)=2(x-4)^4+4(x-4)+12[/tex]Learn more:Transformations in real life problems: