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

g(x) is shifted 4 units right and 6 units up from f(x).

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

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

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

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Verified Answer :

rdevore99 rdevore99 · Answer 1 · 2016-12-14T14:53:22-05:00

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

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tardymanchester tardymanchester · Answer 2 · 2019-03-07T23:22:25-05:00

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).