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If [tex]$G(x)=\frac{1}{x}$[/tex] were shifted 4 units to the left and 4 units up, what would the new equation be?

A. [tex]$G(x)=\frac{1}{(x-4)}+4$[/tex]
B. [tex]$G(x)=\frac{1}{(x+4)}+4$[/tex]
C. [tex]$G(x)=\frac{1}{x}+8$[/tex]
D. [tex]$G(x)=\frac{1}{x}-8$[/tex]

Sagot :

GinnyAnswer
To determine the new equation when the function \( G(x) = \frac{1}{x} \) is shifted 4 units to the left and 4 units up, follow these steps:

1. Horizontal Shift: A shift to the left by 4 units means replacing \( x \) with \( x + 4 \) in the function. This horizontal shift modifies the original function \( G(x) = \frac{1}{x} \) to become \( G(x) = \frac{1}{x+4} \).

2. Vertical Shift: A shift upward by 4 units means adding 4 to the entire function. Thus, the function \( G(x) = \frac{1}{x+4} \) becomes \( G(x) = \frac{1}{x+4} + 4 \).

So, combining these transformations, the new function is:
[tex]\[ G(x) = \frac{1}{x+4} + 4 \][/tex]

Therefore, the correct choice is:

B. [tex]\( G(x) = \frac{1}{(x+4)} + 4 \)[/tex]
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