Given:The function is:[tex]f(x)=x^2[/tex]The graphs of functions [tex]f(x)[/tex] and [tex]g(x)[/tex].To find:The function [tex]g(x)[/tex].Solution:We have,[tex]f(x)=x^2[/tex]The function [tex]f(x)[/tex] is vertically compresses to get the graph of the function [tex]g(x)[/tex]. So, the function [tex]g(x)[/tex] is:[tex]g(x)=kf(x)[/tex][tex]g(x)=kx^2[/tex] ...(i)From the given graph it is clear that the graph of the function [tex]g(x)[/tex] passes through the point (3,3). So, putting [tex]x=3[/tex] and [tex]g(x)=3[/tex] in the above function, we get[tex]3=k(3)^2[/tex][tex]3=9k[/tex][tex]\dfrac{3}{9}=k[/tex][tex]\dfrac{1}{3}=k[/tex]Putting [tex]k=\dfrac{1}{3}[/tex] in (i), we get[tex]g(x)=\dfrac{1}{3}x^2[/tex] Therefore, the correct option is D.