4. The red graph (1) is the graph of f(x) = log(x). Describe the transformation of the blue function (2) and write the equation of the graph.

Answer:Function [tex]f(x)[/tex] is shifted 1 unit left and 1 unit up.[tex]f(x)\rightarrow f(x+1)+1[/tex]Transformed function [tex]f(x+1)+1=\log(x+1)+1[/tex]Step-by-step explanation:Given:Red graph (Parent function):[tex]f(x)=\log(x)[/tex]Blue graph (Transformed function)From the graph we can see that the red graph is shifted 1 units left and 1 units up.Translation 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]The transformation statement is thus given by:[tex]f(x)\rightarrow f(x+1)+1[/tex]As function [tex]f(x)[/tex] is shifted 1 unit left and 1 unit up.Transformed function is given by:[tex]f(x+1)+1=\log(x+1)+1[/tex]