Given the functions f(x)= 1/x−4 +3 and g(x)=1/x+1 +6 .

which statement describes the transformation of the graph of function f onto the graph of function g?

the graph shifts 5 units right and 3 units down.

the graph shifts 3 units left and 5 units up.

the graph shifts 5 units left and 3 units up.

the graph shifts 3 units right and 5 units down.

ANSWER

The graph shifts 5 units left and 3 units up.

EXPLANATION

The given functions are:

and

We want to transform f(x) so that, it coincide with the g(x).

The required transformation is

Let us see why this works.

The transformation f(x+5)+3 will shift f(x) 5 units left and 3 units up.

The third choice is correct.

Answer with step-by-step explanation:

We are given a function which is to be transformed to another function .

We are to determine whether which statement describes the transformation of the graph of function f onto the graph of function g.

Therefore, the correct answer option is: The graph shifts 5 units right and 3 units up.

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step-by-step explanation: