Question

What is the equation of the function y=3/x translated 4 units to the right and 5 units down

Answer 1

The required equation is
`g(x)=(3)/(x-4)-5`.

Explanation:

The given function is

`y=(3)/(x)`

It can be written as

`f(x)=(3)/(x)`

The transformation of a function is defined as

`g(x)=f(x+a)+b`

Where, a represents the horizontal shift and b represents the vertical shift.

If a>0, then the function f(x) shifts a units left and a<0, then the function f(x) shifts a units right.

If b>0, then the function f(x) shifts b units up and b<0, then the function f(x) shifts b units down.

Since the function translated 4 units to the right and 5 units down, therefore the value of a is -4 and bis -5.

`g(x)=f(x-4)-5`

`g(x)=(3)/(x-4)-5`
`[\because f(x)=(3)/(x)]`

Therefore the required equation is
`g(x)=(3)/(x-4)-5`.

Answer 2

Translate 4 units right by replacing x with x-4. Translate down by subtracting that amount from the function.

y = 3/(x -4) -5