To determine the effect of the transformation on the graph of the function [tex]\( f(x) = \frac{1}{x} \)[/tex] when it is transformed to [tex]\( g(x) = \frac{1}{x} - 7 \)[/tex], let's analyze the transformation in detail.
Given the original function:
[tex]\[ f(x) = \frac{1}{x} \][/tex]
The transformed function is:
[tex]\[ g(x) = \frac{1}{x} - 7 \][/tex]
This transformation involves subtracting 7 from the original function [tex]\( f(x) \)[/tex].
The subtraction of a constant from the entire function [tex]\( f(x) \)[/tex] results in a vertical shift of the graph. Subtracting a positive constant [tex]\( c \)[/tex] from the function [tex]\( f(x) \)[/tex] results in shifting the graph of [tex]\( f(x) \)[/tex] down by [tex]\( c \)[/tex] units because every point on the graph is moved down by that constant amount.
In this case, since we are subtracting 7, the entire graph of [tex]\( f(x) \)[/tex] will be shifted downward by 7 units.
Thus, the correct description of the transformation is that the graph is shifted 7 units down.
Therefore, the correct option is:
B. The graph of [tex]\( M(x) \)[/tex] is shifted 7 units down.
