x f x 1 - 64 2 0 3 64 For the linear function f , the table shows three

Question

x f x 1 - 64 2 0 3 64 For the linear function f , the table shows three values of x and their corresponding values of f x . Function f is defined by f x = a x + b , where a and b are constants. What is the value of a - b ?

Accepted Answer

Choice D is correct. The table gives that f ( x ) = 0 when x = 2 . Substituting 0 for f x and 2 for x into the equation f ( x ) = a x + b yields 0 = 2 a + b . Subtracting 2 a from both sides of this equation yields b = - 2 a . The table gives that f ( x ) = - 64 when x = 1 . Substituting - 2 a for b , - 64 for f x , and 1 for x into the equation f ( x ) = a x + b yields - 64 = a 1 + - 2 a . Combining like terms yields - 64 = - a , or a = 64 . Since b = - 2 a , substituting 64 for a into this equation gives b = - 2 64 , which yields b = - 128 . Thus, the value of a - b can be written as 64 - ( - 128 ) , which is 192 . Choice A is incorrect. This is the value of a + b , not a - b . Choice B is incorrect. This is the value of a - 2 , not a - b . Choice C is incorrect. This is the value of 2 a , not a - b .

$x$	$f (x)$
$1$	$negative 64$
$2$	$0$
$3$	$64$

Question x-f-x-