Question

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

Answer 1

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

y = 3/(x -4) -5

Answer 2

Answer:

The required equation is $g(x)=\frac{3}{x-4}-5$.

Step-by-step explanation:

The given function is

$y=\frac{3}{x}$

It can be written as

$f(x)=\frac{3}{x}$

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.

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

$g(x)=\frac{3}{x-4}-5$                         $[\because f(x)=\frac{3}{x}]$

Therefore the required equation is $g(x)=\frac{3}{x-4}-5$.