The graph of the reciprocal parent function f(x)=1/x, is shifted 6 units down and 1 unit to the right to create the graph of g(x). What function is g(x)?
A. g(x)=1/x+6-1
B. g(x)=1/x-1-6
C. g(x)=1/x-6-1
D. g(x)=1/x+1-6

Transformations are used to move a function from one position to another. The new function g(x) is [tex]g(x) = \frac{1}{x-1} - 6[/tex]

Given that

[tex]f(x) = \frac 1x[/tex]

When shifted 6 units down. the rule of transformation is:

[tex](x,f(x)) \to (x,f(x) - 6)[/tex]

So, we have:

[tex]f'(x) = f(x) - 6[/tex]

[tex]f'(x) = \frac 1x - 6[/tex]

When shifted 1 unit left. the rule of transformation is:

[tex](x,g(x)) \to (x -1,f'(x))[/tex]

So, we have:

[tex]g(x) = f'(x - 1)[/tex]

[tex]g(x) = \frac{1}{x-1} - 6[/tex]

Hence, the new function g(x) is [tex]g(x) = \frac{1}{x-1} - 6[/tex]

Read more about function transformation at:

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The graph of the reciprocal parent function f(x)=1/x, is shifted 6 units down and 1 unit to the right to create the graph of g(x). What function is g(x)? A. g(x)=1/x+6-1 B. g(x)=1/x-1-6 C. g(x)=1/x-6-1 D. g(x)=1/x+1-6

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The graph of the reciprocal parent function f(x)=1/x, is shifted 6 units down and 1 unit to the right to create the graph of g(x). What function is g(x)?
A. g(x)=1/x+6-1
B. g(x)=1/x-1-6
C. g(x)=1/x-6-1
D. g(x)=1/x+1-6