Testing a battery's performance and reserve (or amp-hour) capacity is not just a matter of seeing whether it will hold a charge (or checking the electric eye found on some batteries to see if it is green), so testing is best done by an auto technician at a repair shop. A professional can also determine if any problems you are having may be caused by something else, like your battery terminals or alternator. If a bad battery is the culprit, your mechanic will help you choose and install an appropriate replacement.
Alternator: now this was a breakthrough!! Before the alternator was the dynamo-machine. A DC generator who wasn't that bad, but had a lot of glitches, the regulator system was complicated, it was large and in some cars highly unreliable. Then came the alternator. It was brilliantly constructed, highly dependable, half the size of the dynamo and very easy to repair. The output that it gave was much more stable and consistent thus allowing more appliances to be put in the car.
Engine deposits caused by low-quality or contaminated gasoline create drivability problems, and the cure for that might be a fuel system cleaning, either by a repair shop or with a gas-tank additive. An illuminated check engine light signals when something is amiss in the emissions control system, but depending on what the issue is it could also affect fuel economy or engine performance, so don’t ignore it. A faulty oxygen sensor, for example, leaves the engine computer in the dark about how to set the air-fuel mixture, and that can result in poor fuel economy.
A dirty or clogged engine air filter is more likely to reduce acceleration than fuel economy, according to tests conducted by the EPA. Because filters get dirty gradually over time, you might not notice a small but steady loss of performance until your car is accelerating like a turtle. But if you haven’t changed the filter in a couple of years (or sooner in areas that have a lot of soot in the air), that could be part of the problem.