Remove Linear Good From Quasi-linear Utility Function Given a quasi-linear utility function: $u(x_1, x_2) = f(x_1) + \beta x_2$,  $\beta &gt; 0 $

What would happen if good 2 ($x_2$) is removed from the market? Would the new utility function be: $u(x_1) = f(x_1)$? If so, would the demand function simply be $x_1 = m/p_1$? I want to find the new demand function as well as the new indifference curves and draw these in a diagram, but I am unsure how to proceed. Surely I cannot graph them in $x_1, x_2$ space if there is no more $x_2$. Or would I still graph them in $x_1, x_2$ space as vertical lines?

I hope my question is understandable, thx for any help.
This is one possible interpretation. Good 2 being removed from the market can simply be interpreted as $x_2 = 0$. In an economic interpretation the good does not simply disappear from the utility function in the sense that preferences do not change, it is just the availability of the good that changes. This is an external condition, so you can simply think of this as a market constraint $x_2 = 0$. 

Now, looking at indifference curves as the different bundles for which the consumer obtains the same level of utility, and defining this level as $k$. It is clear that for any $k$ when there is only one good, each "indifference curve" will consist of only one point (in particular $x_{1}|u(x_1,0) = k$). In a 2-D graph this will simply correspond some point ($x_1$,0) for each $k$ level. 

The demand function should be quite straightforward.