Hard Functions Problem with Solutions for the SAT Today I will give several solutions to the problem I posted yesterday. Use this link to see the question: Hard Function Problem for the SAT This problem is from the book 28 SAT Math Lessons – Advanced Course. Here is the problem one more time, followed by three methods of solution. Level 5 Functions For which of the following functions is it true that f(-x) = f(x) for all values of x ? A) f(x) = x2 + 5 B) f(x) = x2 + 5x C) f(x) = x3 + 5x D) f(x) = x3 + 5 Solution by picking numbers: Let’s choose a value for x, say x = 2. We compute f(-2) and f(2) for each answer choice. f(-2) f(2) A) 9 9 B) -6 14 C) -18 18 D) -3 13 Since choices (B), (C), and (D) do not match up, we can eliminate them. The answer is therefore choice (A). Important note: (A) is not the correct answer simply because both computations gave the same answer. It is correct because all 3 of the other choices did not work. You absolutely must check all four choices! * Quick solution: We are looking for an even function. Each answer choice is a polynomial. Therefore, the answer is the one with only even powers of x. This is choice (A) (remember that 5 = 5x0 ). Note: See the following post for more information on this method: Even and Odd Functions Graphical solution: Begin putting each of the four answer choices into your graphing calculator (starting with choice (B) or (C)), and choose the one that is symmetrical with respect to the y-axis. This is choice (A). Note: Again, see this post for more information: Even and Odd Functions More SAT and ACT Math Problems with Explanations If you are preparing for the SAT, ACT, or an SAT math subject test, you may want to take a look at the Get 800 collection of test prep books. And if you liked this article, please share it with your Facebook friends: Comments comments