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2-102.

Sketch the graph of $f(x)=\frac{1}{x-4}$. Let $g(x)=f(x+2)-1$. Write an explicit equation for $g(x)$ and sketch its graph. 2-102 HW eTool (Desmos)

Sketch a rational function with an asymptote at $x=4$.

$f\left(x+2\right)-1=\frac{1}{\left(x+2\right)-4}-1$

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2-102 HW eTool (Desmos)