Answer:
Option 4- Graph of g(x) is shifted 4 units left and 6 units down from f(x).
Step-by-step explanation:
Given : Graph of [tex]g(x)=\frac{1}{x+4}-6[/tex]
To find : How does the graph of g(x) compare to the graph of the parent function [tex]f(x)=\frac{1}{x}[/tex]
Solution :
The graph f(x) is being translated to form the graph g(x).
In graph [tex]g(x)=\frac{1}{x+4}-6[/tex] there is
Translation of 4 unit left and 6 unit downward.
In graph f(x) if we shift the graph with 4 unit left it form
f(x)→f(x+b) , the function is shifted towards left with b unit.
So, [tex]f(x)=\frac{1}{x+4}[/tex]
In graph f(x) if we shift the graph with 6 unit downward it form
f(x)→f(x)-a , the function is shifted downward with a unit.
So, [tex]f(x)=\frac{1}{x+4}-6[/tex]
Therefore, Option 4 is correct.
Graph of g(x) is shifted 4 units left and 6 units down from f(x).
