If the point (15/4,7) should have read (15/4,17) then a plot of these points appears to show a hyperbola and the x and y (f(x)) axes look like asymptotes. If the general function has the form f(x)=a/x, then there should be a consistent value for a which can be found be substituting the points in the equation. Take one point (17,15/4) and we get 15/4=a/17, from which a=255/4. f(x)=255x/4. We have no negative values as examples so we cannot assume that the function is defined for negative values of x. f(x)=255x/4 fits all the points except for (15/4,7), which is possibly mistyped. The domain of the function is therefore all values of x>0 and the range of f(x) is f(x)>0, assuming continuity and extrapolation of the function.
If the point (15/4,7) is valid then f(x) as defined above is invalid or incomplete. f(x) may be a piecewise function where f(x)=7 if and only if x=15/4. For 0<x<15/4 and x>15/4, f(x)=255x/4. These would be the domain for x. The range of f(x) is f(x)>0 and f(x)=7 only when x=15/4.