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What’s that weird symbol mean?
Invariably, one kind of question on the SAT causes students to shut down and run away in fear. I’m talking about the Weird Symbol Function question. Let’s take a look!
“I’ve never seen that before,” students say when they see Weird Symbol Functions, and I have to remind them: “Yes, you have. All it is a function…call it f(x) or y= if you like. They’re just telling you what x is and where to plug it in.” Don’t shut down when you see a question like this:
Let x∆ be defined as (x+1)(x-1). Which of the following equals 6∆-5∆?
(A) 2∆+1∆
(B) 3∆+2∆
(C) 4∆+3∆
(D) 5∆+4∆
(E) 6∆+5∆
Oh, no! A triangle! What on earth could it mean?
All it means is this: when you see something next to a triangle, that something is x, and you’re supposed to plug it in exactly where x appears in the definition.
To solve 6∆-5∆, first we need to figure out what 6∆ is. Using our definition, we plug 6 in for x:
x∆ = (x+1)(x-1)
6∆ = (6+1)(6-1)
6∆ = (7)(5)
6∆ = 35
Now let’s find 5∆ using the same definition:
x∆ = (x+1)(x-1)
5∆ = (5+1)(5-1)
5∆ = (6)(4)
5∆ = 24
So 6∆-5∆ = 35-25 = 11.
So now we pick the answer choice that equals 11. To do so, we’ve got to run all the answer choices through the same definition.
When we get to B, we get the following:
3∆+2∆
3∆=(3+1)(3-1)
3∆=(4)(2)
3∆=8
2∆=(2+1)(2-1)
2∆=(3)(1)
2∆=3
8+3=11.
So (B) is our answer!
This principle can be used to solve even the toughest symbol function questions.
These questions are simply testing your ability to PLUG THINGS IN in the right places. As long as you understand what to plug in and where, using the definition–and as long as you don’t make mistakes on your algebra, you’ll be fine!
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