SAT Mathematics Practice Test 4

Since $\mathit{f}\left(\mathit{x}\right)=\frac{3}{2}\mathit{x}+\mathit{b}$ and $\mathit{f}\left(6\right)=7$, substituting $6$ for $\mathit{x}$ in $\mathit{f}\left(\mathit{x}\right)=\frac{3}{2}\mathit{x}+\mathit{b}$ gives $\mathit{f}\left(6\right)\frac{3}{2}\left(6\right)+\mathit{b}=7.$ Then, solving the equation $\frac{3}{2}\left(6\right)+\mathit{b}=7$ for b gives $\frac{18}{2}+\mathit{b}=7$, or $9+\mathit{b}=7.$ Thus, $\mathit{b}=7-9=-2.$ Substituting this value back into the original function gives $\mathit{f}\left(\mathit{x}\right)=\frac{3}{2}\mathit{x}-2;$ therefore, one can evaluate $\mathit{f}\left(-2\right)$ by substituting $-2$ for $\mathit{x}:\frac{3}{2}\left(-2\right)-2=-\frac{6}{2}-2=-3-2=-5$
Choice B is incorrect as it is the value of b, not of f(−2). Choice C is incorrect as it is the value of $\mathit{f}\left(2\right)$, not of $\mathit{f}\left(-2\right).$ Choice D is incorrect as it is the value of $\mathit{f}\left(6\right),$ not of $\mathit{f}\left(-2\right).$