SAT Mathematics Practice Test 6

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 $\mathit{t}\left(\mathit{x}\right).$ For instance, the first row gives $\mathit{x}=1$ and the corresponding values $\mathit{w}\left(1\right)=-1$ and $\mathit{t}\left(1\right)=-3.$ The row in the table where $\mathit{x}=2$ is the only row that has the property $\mathit{x}=\mathit{w}\left(\mathit{x}\right)+\mathit{t}\left(\mathit{x}\right):2=3+\left(-1\right).$ Therefore, choice B is the correct answer
Choice A is incorrect because when $\mathit{x}=1$, the equation $\mathit{w}\left(\mathit{x}\right)+\mathit{t}\left(\mathit{x}\right)=\mathit{x}$ is not true. According to the table, $\mathit{w}\left(1\right)=-1$ and $\mathit{t}\left(1\right)=-3.$ Substituting the values of each term when $\mathit{x}=1$ gives $-1+\left(-3\right)=1,$ an equation that is not true. Choice C is incorrect because when $\mathit{x}=3,$ the equation $\mathit{w}\left(\mathit{x}\right)+\mathit{t}\left(\mathit{x}\right)=\mathit{x}$ is not true. According to the table, $\mathit{w}\left(3\right)=4$ and $\mathit{t}\left(3\right)=1.$ 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 $\mathit{x}=4,$ the equation $\mathit{w}\left(\mathit{x}\right)+\mathit{t}\left(\mathit{x}\right)=\mathit{x}$ is not true. According to the table,$\mathit{w}\left(4\right)=3$ and $\mathit{t}\left(4\right)=3.$ Substituting the values of each term when $\mathit{x}=4$ gives $3+3=4,$ an equation that is not true.