The term “affordable housing” has been used to describe so many things its meaning has been grayed beyond recognition.

Is it for homeless people? Poor people? Is it for young families who cannot afford more space? Is it for people who work, but who cannot afford housing near their jobs?

Despite the term’s amorphous definition, concerns about the cost of housing in Washington are rising about as fast as the rents have in recent years.

The effects are being felt by residents across the economic spectrum. The District family homeless shelter is beset with problems. A central plan for developing more affordable units in the city has stalled. Millenial couples with dual incomes are considering relocation to lower cost areas.

The issue hasn’t gone unnoticed by Mayor Vincent C. Gray. He has committed to building or preserving 10,000 affordable units by 2020, following the recommendation of a housing task force he assembled early in his administration. He has committed $100 million to the effort. And he unsuccessfully tried to get the federal Height Act lifted, which could have increased housing supply over the long term.

With fewer than four months remaining in office, Gray’s staff says the mayor is already more than halfway to the 10,000 goal, with 5,938 units built or under construction. They tally a pipeline of another 5,861 units he would like to see built or preserved.

Where are all of those units? The mayor’s staff breaks it down by three levels of affordability, each measured against the median income for a family of four in the region (currently $107,000).

First, the progress on units for earners at the lowest end of the spectrum:

Here’s a map of units for slightly higher earners:

Lastly a map of units often referred to as “workforce” housing because of their higher income limits:

Still, there are a number of criticisms of Gray’s work on affordable housing.

First, some charge that the mayor acted far too slowly in addressing the problem given the record-setting boom in luxury apartment buildings and the influx of recent college graduates willing to pay higher rent. Many of the projects listed as “completed” in the above maps did not begin with Gray, but then that argument cuts both ways.

For instance, had the city’s inclusionary zoning rule (requiring 8 percent of units in most new projects to be offered below market rate) been implemented more quickly before his arrival, Gray’s results would likely look much better.

Secondly, critics say few units are being preserved or built west of Rock Creek Park. And third, much of the pipeline relies on the success of the New Communities Initiative, a much-delayed program to tear down public housing and replace it with more dense neighborhoods of mixed-used housing and other difficult-to finance projects.

If the District government and the D.C. Housing Authority successfully redevelops these neighborhoods, including Barry Farm in Anacostia and Park Morton off of Georgia Avenue, it would add or preserve hundreds of more units at lower levels of affordability. So far, even the units that have been built through those programs have come at great cost — politically and financially — and critics suggest more could be done to preserve or upgrade existing units.

Follow Jonathan O’Connell on Twitter: @oconnellpostbiz