SAT Mathematics Practice Test 5

Because f is a linear function of x, the equation $\mathit{f}\left(\mathit{x}\right)=\mathit{m}\mathit{x}+\mathit{b},$ where m and b are constants, can be used to define the relationship between x and $\mathit{f}\left(\mathit{x}\right)$. In this equation, m represents the increase in the value of $\mathit{f}\left(\mathit{x}\right)$ for every increase in the value of x by 1. From the table, it can be determined that the value of $\mathit{f}\left(\mathit{x}\right)$ increases by 8 for every increase in the value of x by 2. In other words, for the function $\mathit{f}$ the value of m is $\frac{8}{2}$, or 4.The value of b can be found by substituting the values of x and $\mathit{f}\left(\mathit{x}\right)$ from any row of the table and the value of m into the equation $\mathit{f}\left(\mathit{x}\right)=\mathit{m}\mathit{x}+\mathit{b}$ and solving for b. For example, using $\mathit{x}=1,\mathit{f}\left(\mathit{x}\right)=5,$ and $\mathit{m}=4$ yields $5=4\left(1\right)+\mathit{b}.$ Solving for b yields $\mathit{b}=1.$ Therefore, the equation defining the function f can be writtenin the form $\mathit{f}\left(\mathit{x}\right)=4\mathit{x}+1.$