The function f(x) = xis translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)?

Answer:[tex]g(x)=x+4[/tex]Step-by-step explanation:Given[tex]f(x)=x[/tex][tex]g(x)\rightarrow f(x)[/tex] shifted 7 units left  and 3 units downTranslation Rules:[tex]f(x)\rightarrow f(x+c)[/tex]If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the left.If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the right.[tex]f(x)\rightarrow f(x)+c[/tex]If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the up.If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the down.Applying the rules to [tex]f(x)[/tex][tex]f(x)\rightarrow f(x+7)[/tex]            [7 units left][tex]f(x+7)\rightarrow f(x+7)-3[/tex]    [3 units down]∴ [tex]g(x)=f(x+7)-3=(x+7)-3=x+7-3=x+4[/tex][tex]g(x)=x+4[/tex]