For which of the following functions is f(-1/2) > f(2)?

A. f(x) = 3*x^2

B. f(x) = 3*x

C. f(x) = 3 + x^2

D. f(x) = 3 + 1/x

E. f(x) = 3/x^2

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Students get confused on these type of questions sometimes because we aren’t generally used to plugging into answer choices TWICE. But that’s what you have to do for each answer choice. You have to plug in -1/2 and then also plug in 2, and see is the result when you plug in -1/2 is greater than the result when you plug in 2. This will only be true for ONE answer choice in this Magoosh question.

A. f(x) = 3*x^2

If x = -1/2, then f(x) = 3/4.
If x = 2, then f(x) = 12.

Is 3/4 > 12? Nope! Cross this one off.

B. f(x) = 3*x

If x = -1/2, then f(x) = -3/4.
If x = 2, then f(x) = 6.

Is -3/4 > 6? Nope!

C. f(x) = 3 + x^2

If x = -1/2, then f(x) = 3.25
If x = 2, then f(x) = 7

Is 3.25 > 7? No!

D. f(x) = 3 + 1/x

If x = -1/2, then f(x) = -2
If x = 2, then f(x) = 3.5

Is -1/2 > 3.5? Nope.

E. f(x) = 3/x^2

If x = -1/2, then f(x) = 12
If x = 2, then f(x) = 3/4

Is 12 > 3/4? Yes! We finally have an answer!

Even though it’s a PS question, it kind of has that Data Sufficiency vibe in which you’re testing cases. Here we had to “test out” each of the answer choices and see which one gave us the relationship we were looking for.