Functions as symbols – SAT Algebra Tip 4

Ever see those weird symbol questions on the SAT? Something to the tune of “if xΩ = 2x-1, then what is the value of 3Ω?” You freeze and think to yourself—we haven’t covered horseshoes yet in precalc!

1) The “weird symbols” questions are really functions in disguise. Whenever you see a weird symbol, its corresponding relationship (here, 2x-1) will ALWAYS be defined immediately after. So don’t worry if you haven’t covered horseshoes yet. In fact, most of the time you can substitute f(x) for the weird symbol. The question above could be rewritten as, “if f(x)=2x-1, what is f(3)?” So take these questions and treat them exactly like functions. Just the same as a function could be called “f(x), g(x) or h(x),” why couldn’t it be called xΩ?

2) The horseshoe, spade, weird brackets, smiley face, triangle and whatever other strange symbols that show up on the exam have no actual defined mathematical meaning. No theoretical mathematician knows what xΩ is either! That’s why it will always be defined for you.

3) Sometimes the SAT is testing your ability to draw visual parallels . For instance, take the following question:

Because there is no triangle in real mathematics, only in SAT land, the SAT wants to see if you reason—“hmm, in the example, the lower left-hand number (a) was multiplied by the top number (b) and then the lower right-hand number (c) gets subtracted from that product. Maybe I should do the same thing to the numbers in the question! In which case, (7(3)-2) = 21-2 = 19.

QUICK TIP: When you see strange symbols, don’t freak out, treat them as functions, and be on the lookout for visual parallels in how the variables are spatially laid out.