x f x - 4 0 - 19 5 1 - 18 5 2 For the linear function f ,

Question

x f x - 4 0 - 19 5 1 - 18 5 2 For the linear function f , the table shows three values of x and their corresponding values of f x . If h x = f x - 13 , which equation defines h ?

Accepted Answer

Choice B is correct. An equation that defines a linear function f can be written in the form f x = m x + b , where m and b are constants. It's given in the table that when x = - 4 , f x = 0 . Substituting - 4 for x and 0 for f x in the equation f x = m x + b yields 0 = m - 4 + b , or 0 = - 4 m + b . Adding 4 m to both sides of this equation yields 4 m = b . Substituting 4 m for b in the equation f x = m x + b yields f x = m x + 4 m . It's also given in the table that when x = - 19 5 , f x = 1 . Substituting - 19 5 for x and 1 for f x in the equation f x = m x + 4 m yields 1 = m - 19 5 + 4 m , or 1 = 1 5 m . Multiplying both sides of this equation by 5 yields m = 5 . Substituting 5 for m in the equation f x = m x + 4 m yields f x = 5 x + 4 5 , or f x = 5 x + 20 . If h x = f x - 13 , substituting 5 x + 20 for f x in this equation yields h x = 5 x + 20 - 13 , or h x = 5 x + 7 . Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is an equation that defines the linear function f , not h .

$x$	$f (x)$
$negative 4$	$0$
$- \frac{19}{5}$	$1$
$- \frac{18}{5}$	$2$

Question x-f-x-