The required function is to be shifted the given units.
The equation of the translated graph is [tex]g(x)=\dfrac{1}{x+2}+3[/tex]
The given function is [tex]y=\dfrac{1}{x}[/tex]
The upward translation is represented by
[tex]f(x)+a[/tex]
Here,
a = 3
The leftward translation is represented by
[tex]f(x+b)[/tex]
here,
b = 2
[tex]f(x+2)+3=\dfrac{1}{x+2}+3\\\Rightarrow g(x)=\dfrac{1}{x+2}+3[/tex]
The translated function is [tex]g(x)=\dfrac{1}{x+2}+3[/tex]
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