The table above shows some values of the functions w and t. For which value of x is w(x) + t(x) = x ?

Options

A. 1
B. 2
C. 3
D. 4

Answer

B

Explanation

This question can be answered by making a connection between the table and the algebraic equation. Each row of the table gives a value of x and its corresponding values in both w(x) and t(x). For instance, the first row gives x = 1 and the corresponding values w(1) = −1 and t(1) = −3. The row in the table where x = 2 is the only row that has the property x = w(x) + t(x): 2 = 3 + (−1). Therefore, choice B is the correct answer.
Choice A is incorrect because when x = 1, the equation w(x) + t(x) = x is not true. According to the table, w(1) = −1 and t(1) = −3. Substituting the values of each term when x = 1 gives −1 + (−3) = 1, an equation that is not true. Choice C is incorrect because when x = 3, the equation w(x) + t(x) = x is not true. According to the table, w(3) = 4 and t(3) = 1. Substituting the values of each term when x = 3 gives 4 + 1 = 3, an equation that is not true. Choice D is incorrect because when x = 4, the equation w(x) + t(x) = x is not true. According to the table, w(4) = 3 and t(4) = 3. Substituting the values of each term when x = 4 gives 3 + 3 = 4, an equation that is not true.