If fungoes are a ball tossed into the air by a batter and then struck as it comes down then a fungo bat is a baseball bat used for hitting fungoes. To go into more detail, a fungo bat is a long, lightweight baseball bat used by coaches (or parents) during pregame hitting or practice to help them hit grounders and pop flys with more consistency and less fatigue. To be one of the best in baseball, countless hours of practice are a must and fungo bats are intended for both infield and outfield practice. Plus, they help tremendously with control and accuracy so that coaches and parents can place a ball where they want when they want. 
The fungo is used by a coach to hit balls for defense practice. It is lighter weight, so less fatiguing to hit ball after ball. The fungo sheds its weight above the hands. The severely tapered barrel to drops weight and maintains a high moment of inertia. While the bat would be at greater risk of breaking if used in a live batting exercise, it is safe to use in practice because there are much fewer mis-hits.
Fungo bats aren’t typical bats like the ones Mike Trout takes with him to a game situation. Rather, they’re more of practice bats. The bats are specially made for coaches to utilize when testing the fielding of their players. For example, a coach would break out his or her fungo bat when he or she is looking to hit his or her shortstop a couple of ground balls or when he/she hits pop flies to the centerfielder.
Fungo bats are, simply put, a long, skinny, and lightweight baseball bat used for fielding practice. Typically, they are around 34 to 37 inches in length and between 17 and 24 ounces in weight, give or take a couple of ounces. They will also almost always feature a 2 1/4 inch barrel diameter to allow for more control during a swing. As you can tell, fungo bats are longer than a normal baseball bat and much more lightweight in comparison. Most fungo bats are going to be made up of ash wood while there are some maple and bamboo wood fungo bats, some composite wood fungo bats, and very few aluminum alloy fungo bats. Almost all of these designs will be under $100 with very few eclipsing that mark. 
The Wright & Ditsons Lajoie baseball bat. This bat had a normal size barrel but had two knobs on the handle. The lowest knob was at the bottom of the handle and the other knob was roughly two inches above the lowest knob. This was designed to have better spacing between the hands due to the knob being in the middle of the grip. This also gave batters an advantage when they choked up on the bat, because the second knob provided a better grip.
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First base fungo hits fly balls to center field (helps here if both fungo hitters move up and apart, hitting from about the front of the mound extended towards the bases). Center throws to second, second baseman is cutoff (for us it was, anyways - change to suit your style). Third base fungo hits balls to left field, who throw to third, with a second shortstop as cutoff (but you really don't need one, if you're shorthanded).

Fungo golf is a game involving two or more players in which they use fungo bats and baseballs and their object is to hit certain objects at a field. Fungo golf is played very similar to golf, where the player with the fewest strokes after a certain number of holes (typically nine or eighteen) wins the game. While there is no concrete history of how fungo golf was created, it has spread throughout America as a popular game especially with baseball players and coaches.