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]
