The graph below is a vertical and/or horizontal shift of \(y=1/x\) (assume no reflections or compression/expansions have been applied).

(a) The graph’s equation can be written in the form

\begin{equation*}
f(x) = \frac{1}{x+A} + B
\end{equation*}

for constants \(A\) and \(B\text{.}\) Based on the graph above, find the values for \(A\) and \(B\text{.}\)

\(A =\) and \(B =\)

(b) Now take your formula from part (a) and write it as the ratio of two linear polynomials of the form,

\begin{equation*}
f(x) = \frac{M x + C}{x+D}
\end{equation*}

for constants \(M\) , \(C\text{,}\) and \(D\text{.}\) What are the values of \(M\) , \(C\text{,}\) and \(D\text{?}\)

\(M =\) , \(C =\) , and \(D =\)

(c) Complete the exact values of the coordinates of the intercepts of the graph.

\(x\)-intercept:

\(y\)-intercept: