The rules for transforming a function f(x) into a function g(x) are:
g(x) = a·f(b(x-c)) + d where:
a = vertical cmpress (stretch)
b = horizontal dilation (stretch)
c = horizontal (left/right) shift
d = vertical (up/down) shift
[tex]\begin{gathered} For\text{ F(x) = x} \\ g(x)\text{ = a.f(b(x-c))+d} \end{gathered}[/tex][tex]a\text{ = }\frac{1}{5}\text{ , b = 1 , c = 0 }[/tex]Shift up 7 units means d = +7
[tex]g(x)\text{ = }\frac{1}{5}x+7[/tex]Hence the correct answer is Option D
