# Decoding Symbols on the SAT Math Test

One of the most popular (to the test-makers, that is) types of function problems on the SAT involves symbols. In these problems, the SAT-makers create a new symbol for a function.

You can tackle symbols in the following practice questions.

## Practice questions

- If
*a*^*b*= 2*a*–*b*, which of the following is equal to 3 ^ 4?**A.**1**B.**2**C.**3**D.**4

- If

is defined as *x*^{2} – y for all integers *x* and *y*, which of the following is always true?

## Answers and explanations

**B.**Just as in a normal function problem, where you plug in a number for*x,*here you plug in 3 and 4 for*a*and*b.*It’s actually very simple. To solve 3 ^ 4, plug in those numbers, in order:And the answer is Choice (B).

**D.**No cool solving methods here. You just have to check all the possibilities. Choice (A):which equals

*y*only if*y*is 1/2. Moving on to Choice (B):This is positive if

*x*is 2 or more, but if*x*is 1 or 0, then it’s negative. Now for Choice (C):They’re not equal. Which leaves Choice (D):

At last.