Function problems are asked on every SAT Reasoning Test. Many times, these confuse students who aren’t familiar with the new notation. Here we show a three step process that will easily and rapidly lead you to to right answer.

Functions problems will define a new function, usually through some kind of odd symbol. Don’t get confused by the new symbol and translate the original problem into an easier to understand form.

1. Identify what the new function and what each of the variables do in the new function. This will usually be given. Write out the functional form.

2. Look at what you’re being asked to do. Match up the given values with variables in the functional form. Write down each of these matches.

3. Plug into the original function and solve for your variable.

Calculators will almost never be required for this type of problem. If you are forced to use your calculator, most likely you have made a mistake in comprehending the question somewhere. Double check that you have interpreted the new function correctly and have not made any errors in substitution.

Example
? is defined such that x ? y = -xy + x – y. If G ? 3 = 6, then G = ?
A. 9/2
B. 9/4
C. -9/2
D. -9/4
E. -9

1. Here the new function simply means to take the first number, then subtract by the second number and the product of the two numbers.

2. We have x = G, y = 3. Write these equivalencies down! This is the key to not making silly mistakes.

3. Plugging into the equation, we have -3G + G – 3 = 6. If we simplify this algebraic equation, we get -2G = 9 and G = -9/2.

Check your work! These problems are usually very fast but can be easy to make a mistake on. After you get an answer, plug it back in to the original equation to check that it works. In this case, let’s calculate 9/2 ? 3.

Plugging into the equation -xy + x – y, we get -(-9/2)(3) – 9/2 – 3 = 27/2 – 9/2 – 3 = 18/2 – 3 = 9 – 3 = 6. Checking your work after algebra problems like these will save you countless mistakes over the long run.

There you have it! Next time you see a functions problem on the SAT math section, you should have no problems solving it.

More details on common SAT math problems at BulletER. BulletER.com offers comprehensive SAT help for reading, writing, and math free for all students.

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