Answer:
[tex]y=\frac{2}{x+3}+4[/tex]
Step-by-step explanation:
Equation : [tex]f(x) = y= \frac{2}{x}[/tex]
Initially the graph of the given function is translated 3 units to the left
Rule : When the graph is translated by b units to left
So, [tex]f(x)\rightarrow f(x+b)[/tex]
Since we are given that initially the graph is translated 3 units to the left
So, b = 3
So, [tex]\frac{2}{x}\rightarrow \frac{2}{x+3}[/tex]
Now, [tex]f(x) = y =\frac{2}{x+3}[/tex]
Now the graph is again translated by 4 units up.
Rule : When the graph is translated by b units up
So , [tex]f(x)\rightarrow f(x)+b[/tex]
Since we are given that the graph is translated 4 units up
So, b = 4
So, [tex]\frac{2}{x+3}\rightarrow \frac{2}{x+3}+4[/tex]
Thus [tex]f(x)=y=\frac{2}{x+3}+4[/tex]
Hence Option D is correct: [tex]y=\frac{2}{x+3}+4[/tex]
