College Algebra (6th Edition)

(Work done in online calculator desmos.com) Let $f(x)=\displaystyle \frac{1}{x}$ (graph: blue, dashed) $g(x)=\displaystyle \frac{1}{x+1}-2=f(x+1)-2$ So, the graph of $g$ (red, solid line) is obtained by 1. shifting the graph of $f(x)=\displaystyle \frac{1}{x}$ to the left by $1$ unit (graph of $f(x+1)=\displaystyle \frac{1}{x+1}$, green, dashed) and then 2. shifting the graph of $f(x+1)$ downward by 2 units. ( $f(x+1)-2=g(x))$ (A shift to the left or right moves the vertical asymptote A shift up or down moves the horizontal asymptote)