Math: 22fd3e1f

ID: 22fd3e1f

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

Comment: Many avenues can reach the correct answer quickly, so pick a method that is comfortable for you and see it through.

Method 1: Probably the most common way to solve the question, I imagine, would be to work out the algebra. Factor where you can.

(x^3 - 9x)/(x^2 - 2x - 3)

x(x^2 - 9)/(x - 3)(x + 1)

x(x + 3)(x - 3)/(x - 3)(x + 1)

The (x - 3) will cancel out, leaving a hole in the graph. Since the question tells us that x > 3, there is no concern about a vertical asymptote at x = -1. Without (x - 3) on either side of the division bar, what remains looks exactly like answer choice (D). The correct answer is (D).

Method 2: Use Desmos to graph the quotient. 

Now, plug in the answer choices one by one to compare. The correct answer will overlay the graph above.

The black graph is the one we are looking for, so (D) must be the correct answer.

Method 3: Provided you observe the constraint that x > 3, you can plug in a value for x in your calculator and solve. Play a matching game, decimal and all. How about x = 5?

It is hard to go wrong with a calculator that displays all the answers simultaneously. Clearly, the correct answer is (D).