Graph features and asymptotic behaviour of modulus functions

The question asks to identify specific features of the graph of a modulus-based function such as intersection points with asymptotes, axes, or other curves.

turkey-yks 2016 Q39 View
$$f ( x ) = \left| \frac { 2 x - 1 } { x - 1 } \right|$$
The graph of the function intersects its horizontal asymptote at the point (a, b).
Accordingly, what is the sum $a + b$?
A) $\frac { 5 } { 2 }$
B) $\frac { 7 } { 2 }$
C) $\frac { 8 } { 3 }$
D) $\frac { 9 } { 4 }$