SAT Tip: Don't Overthink Function Problems

This tip on improving your SAT score was provided by Rochelle Glazman at Veritas Prep.

If f(x) = x2 + 3 and f(a) = b, which of the following is f(b)?
(A) a2 +3
(B) a2 +6
(C) (a2 +3)2
(D) (a2 +3)2 + 3
(E) a4 + 12

One key point to remember about the SAT math sections is that they are much simpler and straightforward than they appear, so don’t overthink them. First, when reading the question, make sure you have defined all values and you understand what the question is looking for. Function problems generally involve values and information already given in the problem. To solve function problems, take all the information you have, define any values you still can, and then figure out what you need to plug in, and where. Remember that you will rarely have to solve these questions with brute force. The only algebra knowledge they are testing is whether you understand how functions work. The rest is merely plugging in numbers.

Here we have a function defined as f(x) = x2 + 3. We are also given that f(a) = b. Before we start solving anything, we have to define our values, so plug a into the original equation: f(a) = a2 + 3 = b.

Now we have found all the information we could be working with from what we’ve been given. The next step is to figure out exactly what the question is looking for. The question is, which of the following is f(b)?

From the original function, we know that f(b) = b2 + 3. Before you start solving for b and trying to plow through the problem with brute force, remember that SAT math questions are simpler than you think. Review the information we have already been given or found. The answer choices are all in terms of a, so look at the information we have that relates b to a. We previously found that b = a2 + 3.

Therefore, f(b) = b2 + 3 and plugging in a2 + 3 for b in this expression yields (a2 + 3)2 + 3.The answer is D.

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