Answer:
g(x) = log(x) + 4
Step-by-step explanation:
The graph of [tex]g(x)[/tex] is the graph of [tex]f(x)[/tex] shifted along the positive y-direction by 4 units. We know this because [tex]f(x)[/tex] goes flat as it approaches [tex]y =1,[/tex] and [tex]g(x)[/tex] goes flat when [tex]y = 5[/tex]; therefore, the function [tex]g(x)[/tex] is a shifted version of [tex]f(x)[/tex], and it is
[tex]g(x) = f(x)+4[/tex]
[tex]\boxed{g(x) = log(x)+4}[/tex]
We can confirm this by putting [tex]x =1[/tex] into the function, and we get:
[tex]f(1) = log(1) = 0[/tex],
and the graph of [tex]f(x)[/tex] confirms this.
[tex]g(1) = log(1)+4 = 4[/tex],
which the graph of [tex]g(x)[/tex] confirms.
