There are several different types of functions tested on the SAT: linear, quadratic, as well as function questions which ask about domain and range (the ones that look like f(x)). Today we’re going to look at symbol functions. In symbol functions, the SAT test makers choose a new symbol, something that you probably haven’t seen before or at least not in a mathematical equation, and give it a new definition.
Many students get nervous when they see symbol functions because they think they should recognize the new symbol in the same way they do common math symbols like +, -, x and ÷. Remember that the question will tell you exactly how the new symbol functions. While these problems may seem intimidating at first, simple plugging in is usually all that is called for to get the right answer.
Example: Let z € y be defined by the equation z € y = z2 – 1/y. What is the value of 3 € 1?
Here we plug in 3 for z and 1 for y to solve.
Test your SAT math skills with this SAT multiple choice practice question!
32 – 1/1
9 – 1
8
Now let’s take a look at a more challenging question you may have seen on Grockit!
Example: Let the function $x be defined as $x = (x + 3)(x – 3). If $a = a + 3, what is one possible value for a?
A 9
B 6
C 4
D 3
E 0
If you are a little confused about where to start, remember that you can always plug in the answer choices into the function to see which one will yield a + 3. Since the answer choices are listed numerically, let’s start with answer choice C. If our answer is too large, we will be able to eliminate A and B as well. If it’s too small, we’ll eliminate D and E.
C $4 = (4 + 3)(4 – 3)
$4 = (7)(1) = 7
7 does equal 4 + 3, so C must be the correct answer!
Look out for more opportunities to use the answer choices to your advantage on symbol function questions! Plugging in and working backwards is one SAT strategy that really pays off!
Find out how Grockit predicts your score based on your answers and tracks your performances and improvements, projecting accurate score improvements.
