Question

How does the graph of g(x) = 1/x+4-6 compare to the graph of the parent function f(x)=1/x ?

Answer 1

Answer with explanation:

We are given a parent function f(x) as:

       $f(x)=\dfrac{1}{x}$

and the transformed function g(x) is given by:

       $g(x)=\dfrac{1}{x+4}-6$

We know that the transformation of the type:

     f(x) → f(x+a)

is either a shift a units to the left or to the right depending whether a is positive or negative respectively.

Also, the transformation of the type:

   f(x) → f(x)+a

is the shift of the function f(x) either upward or downward depending on whether x is positive or negative respectively.

Here the function g(x) is:

     $g(x)=f(x+4)-6$

This means that the function g(x) is a shift of the function f(x) 4 units to the left and then it is translated 6 units downward.

Also we may see by the graph.

Answer 2

You can recall that
f(x-c) is shifting to the right by c units
f(x+c) is shifting to the left by c units
f(x)+c is shifting up by c units
f(x)-c is shifting down by c units
given that f(x)=1/x
g(x)=f(x+4)-6 thus f(x) is shifted to the left 4 units and down 6 units