Linear functions SAT question

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

Choices A, B, and D are incorrect. Any equation defining the linear function f must give values of f (x) for corresponding values of x, as shown in each row of the table. According to the table, if , . However, substituting into the equation given in choice A gives , or , not 13. Similarly, substituting into the equation given in choice B gives , or , not 13.

Lastly, substituting into the equation given in choice D gives , or , not 13. Therefore, the equations in choices A, B, and D cannot define f.