"Silly Symbol" Formulas (Functions)

Now, the consider the problem again. For every value of _x_ and _y_ different from zero, the operation ¿ is defined as _x_ ¿ _y_ = (_x_ +_y_) / _x_. Which of the following is the equivalent of 3 ¿ 6? To answer the question (and others like it), just __Plug In__ the numbers to the input variable and follow the rule. In this case, you need to __Plug In__ 3 and 6 to the rule you just established. What is the correct answer to this problem?

Incorrect. Make sure to plug in the numbers in the correct order. Remember to divide by _x_, which is the first number.

Incorrect. Check your calculations again.

Correct! __Plug In__ _x_ = 3 and _y_ = 6 into the function _x_ ¿ _y_ = (_x_ + _y_) / _x_: 3 ¿ 6 to get $$\displaystyle (3 + 6) / 3 = 9 / 3 = 3$$.

Regardless of whether the question uses a strange word, the _Monopoly_ top hat, or a cross-eyed rabbit symbol, it will usually tell you what the function does. In other words, it will explain the __rule__. It might be useful to think of a function as a magic box into which you put numbers and then crank the handle and open the box to find the new value. The rule of a function is what the box does to the numbers once the handle is cranked. You can think of functions as consisting of input variables (the number/s you put in the box) and a corresponding output value (the number that comes out of the magic box). In the case of the example above, how would you describe the rule of the function?

To sum up: [[summary]]

Not quite. The rule of this function is to take two given numbers, _x_ and _y_, add them, and divide the sum by the first number.

Exactly!

Every once in a while, the GRE throws a curve ball in the form of a "functions" type question. Consider the following problem: For every value of _x_ and _y_ different from zero, the operation ¿ is defined as _x_ ¿ _y_ = (_x_ +_y_) / _x_. Which of the following is the equivalent of 3 ¿ 6? Such curve ball question types may employ a symbol to label the function (such as the inverted question mark, ¿, in the above example).

When __Plugging In__ values to a function, pay attention to - the order of operations (PEMDAS), and - the order of variables, as presented in the function rule. In the above example of _x_ ¿ _y_ = (_x_ + _y_) / _x_, 3 ¿ 6 is very different from 6 ¿ 3. In the first case, _x_ = 3 and _y_ = 6, and the result comes out as 3. In the second case, _x_ = 6 and _y_ = 3, and the result comes out as $$\displaystyle (6 + 3) / 6 = 9 / 6 = 3/2$$. Keep in mind that the answer choices might include distractors that will capitalize on this fact.

1

3/2

3

It means take two given numbers, _x_ and _y_, add them, and divide the sum by the first number.

It means take two given numbers, _x_ and _y_, add them, and divide the sum by the second number.

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