Question

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

a. y=2/x-3 -4
b. y=2/x+3 -4
c. y=2/x-3+4
d. y=2/x+3 +4

Answer 1

`y=(2)/(x+3)+4`

Explanation:

Equation :
`f(x) = y= (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,
`(2)/(x)\rightarrow (2)/(x+3)`

Now,
`f(x) = y =(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,
`(2)/(x+3)\rightarrow (2)/(x+3)+4`

Thus
`f(x)=y=(2)/(x+3)+4`

Hence Option D is correct:
`y=(2)/(x+3)+4`