Math: 023c0a8d

ID: 023c0a8d 

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)

Comment: You will either get this one within a few seconds or make an assumption right away that will lead to the wrong answer.

Method 1: Match what is inside the parentheses: f(3x) and f(6).

3x = 6

x = 2

f(2) = (2) - 6

f(2) = -4

The correct answer is (B).

Method 2: You could use Desmos, but you would have to understand that if f(3x) = x - 6, then f(x) on its own would be (1/3)x - 6—the coefficient of x does not change the rest of the linear equation. You could now trace the graph when x = 6. I will add a table to show the point in question. (Since I would not recommend going to the trouble to set up a table for a single point, I will avoid explaining the process of setting up a table in this post.)

Once again, it is clear that when x = 6 in the f(x) function, f(x) = -4, and the correct answer is (B).

Method 3: There is no reason to approach the question in any other way besides the two methods outlined above. Plugging in the answers might lead to confusion, as though you should plug in 6 for x to derive (6) - 6 = 0. ((A) would be the answer if x were 0, and (D) would be input value for x to make f(3x) = f(6). Watch those traps, and read the question carefully.)