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The graph of the reciprocal parent function, [tex]\( f(x)=\frac{1}{x} \)[/tex], is shifted 7 units up and 2 units to the right to create the graph of [tex]\( g(x) \)[/tex]. What function is [tex]\( g(x) \)[/tex]?

A. [tex]\( g(x)=\frac{1}{x-7}+2 \)[/tex]

B. [tex]\( g(x)=\frac{1}{x+2}+7 \)[/tex]

C. [tex]\( g(x)=\frac{1}{x-2}+7 \)[/tex]

D. [tex]\( g(x)=\frac{1}{x+7}+2 \)[/tex]

Sagot :

GinnyAnswer
Sure, let's break down the transformation of the function [tex]\( f(x) = \frac{1}{x} \)[/tex] step-by-step.

1. Horizontal Shift:
To shift the graph 2 units to the right, we replace [tex]\( x \)[/tex] with [tex]\( x - 2 \)[/tex]. Hence, our function becomes:
[tex]\[ f(x - 2) = \frac{1}{x - 2} \][/tex]

2. Vertical Shift:
To shift the graph 7 units up, we add 7 to the function. So, the transformed function becomes:
[tex]\[ g(x) = \frac{1}{x - 2} + 7 \][/tex]

Putting it together, the function [tex]\( g(x) \)[/tex] after shifting 7 units up and 2 units to the right is:
[tex]\[ g(x) = \frac{1}{x - 2} + 7 \][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
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