Tuesday’s S&P/Case-Shiller home-price indexes show a market in which U.S. home prices are still falling, but not as dramatically as in previous months. This is good news for homeowners and home sellers since it indicates that the market is bottoming out. It’s also a sign that the housing downturn, now in its fifth year, may be approaching the end. Nationally, the average sale price of a single-family home fell 1.9% from a year ago, which economists are calling effectively flat. Some markets, including Phoenix, showed major growth in prices, while five of them — Atlanta, Chicago, Las Vegas, New York and Portland — fell to new post-financial crisis lows. Analysts took the news that the Case-Shiller indices, which trail the market by three months, are finally coming around to the fact that the market, generally speaking, is at or near bottom. They remain divided, however, on whether we are likely to see continued improvement in the short term.