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Verified Answer :

Answer:

\(y=\frac{2}{x+3}+4\)

Step-by-step explanation:

Equation : \(f(x) = y= \frac{2}{x}\)

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,  \(f(x)\rightarrow f(x+b)\)

Since we are given that initially the graph is translated 3 units to the left

So, b = 3

So,   \(\frac{2}{x}\rightarrow \frac{2}{x+3}\)

Now,   \(f(x) = y =\frac{2}{x+3}\)

Now the graph is again translated by 4 units up.

Rule : When the graph is translated by b units up

So ,   \(f(x)\rightarrow f(x)+b\)

Since we are given that the graph is translated 4 units up

So, b = 4

So,   \(\frac{2}{x+3}\rightarrow \frac{2}{x+3}+4\)

Thus    \(f(x)=y=\frac{2}{x+3}+4\)

Hence Option D is correct: \(y=\frac{2}{x+3}+4\)

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