Question

What is the equation of the function y=2/x translated 3 units to the left and 4 units up?

Answer 1

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: $y=\frac{2}{x+3}+4$

Answer 2

It would be A, because I remember working on the same question