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:

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  $g(x)=\frac{1}{x+4}-6$        

To find : How does the graph of g(x) compare to the graph of the parent function $f(x)=\frac{1}{x}$

Solution :  

The graph f(x) is being translated to form the graph g(x).

In graph $g(x)=\frac{1}{x+4}-6$ 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, $f(x)=\frac{1}{x+4}$

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, $f(x)=\frac{1}{x+4}-6$

Therefore, Option 4 is correct.

Graph of g(x) is shifted 4 units left and 6 units down from f(x).

         

Answer 2

g(x) is shifted 4 units left and 6 units down from f(x).