Question

The graph of y = 3/x is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph of f(x)?

Answer 1

Answer: The required equation of f(x) is $f(x)=-\frac{3}{x} -2$.

Explanation:

The given equation is,

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

If the graph reflects across the y-axis then,

$(x,y)\rightarrow (-x,y)$

It means the y coordinate is same and the sign x coordinate changed.

So, the equation of given graph after reflection across the y axis is,

$y_1=\frac{3}{-x}$

After reflection the graph shifts 2 unit down.

If a graph translate 2 unit down then,

$(x,y)\rightarrow (x,y-2)$

So, the function f(x) is,

$f(x)=y_1-2$

$f(x)=\frac{3}{-x}-2$

$f(x)=-\frac{3}{x}-2$

Therefore the equation of f(x) is $f(x)=-\frac{3}{x} -2$.

Answer 2

ANSWER

Given

The equation is

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

The equation of a rectangular hyperbola is xy = c²

where c is constant

thus  above  is the equation of the rectangular hyperbola.

First case

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

the graph of this equation is shown below.  

Second case

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

is reflected over the y -axis

than the equation becomes

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

the graph is shown below.  

Third Case

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

translated down 2 units to form f(x)

than the equation becomes

$y-2 =\frac{-3}{x}$

The graph is shown below.