PSAT Math Multiple-Choice Question 163: Answer and Explanation

Question: 163

Which of the following is an equivalent form of rational function g that displays as constants or coefficients values that are not part of the domain?

• A.
• B.
• C.
• D.

Correct Answer: D

Explanation:

D

The question asks for an equivalent form of the function that displays values not included in the domain as constants or coefficients. Determine what is not in the domain. In a rational function, a value of x is not in the domain if it makes the denominator equal to 0. To find these values, set the denominator equal to 0 to get 3x² - 3x - 18 = 0. To get the roots of the quadratic, put the quadratic in factored form. Therefore, the correct answer must have the denominator written in factored form. Factor 3 from 3x² - 3x - 18 to get 3(x² - x - 6). Now factor (x² - x - 6) to get 3(x - 3)(x + 2). Therefore, the denominator must be written in the form 3(x - 3)(x + 2). Eliminate (A), (B), and (C), which don't include this. The correct answer is (D).