The graph of the tangent function approaches vertical asymptotes at x=±π/2. The inverse function will have horizontal asymptotes of y=±π/2. The only viable choice among your graphs is ...
... Graph C
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The graph of the inverse of a function is the function's graph with the x- and y-coordinates swapped. Essentially, the graph is reflected across the line y=x. The graph of the tangent function has a vertical aspect. Its inverse has a horizontal aspect.