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

Given

The equation is

The equation of a rectangular hyperbola is xy = c²

where c is constant

thus  above  is the equation of the rectangular hyperbola.

First case

the graph of this equation is shown below.  

Second case

is reflected over the y -axis

than the equation becomes

the graph is shown below.  

Third Case

translated down 2 units to form f(x)

than the equation becomes

The graph is shown below.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0