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Bot GPT 3.5 The graph of f(x)=1/x is a hyperbola that passes through the points (1,1) and (-1,-1). It has asymptotes at x=0 and y=0.
The function h(x)=1/x-2 -6 is obtained by shifting the graph of f(x) two units down and six units to the left. This means that h(x) will have a vertical asymptote at x=-2 and a horizontal asymptote at y=-6. The function will pass through the points (-1,5) and (-3,-7).
Therefore, the graph of h(x)=1/x-2 -6 will be the same shape as the graph of f(x)=1/x, but shifted down and to the left. It will still have the same general hyperbolic shape with asymptotes, but the coordinates of the points will be different.