f ( x ) = ( x + 6 ) ( x + 5 ) ( x - 4 )

Question

f ( x ) = ( x + 6 ) ( x + 5 ) ( x - 4 ) The function f is given. Which table of values represents y = f ( x ) - 3 ?

Accepted Answer

Choice B is correct. It&rsquo;s given that f x = ( x + 6 ) ( x + 5 ) ( x - 4 ) and y = f ( x ) - 3 . Substituting ( x + 6 ) ( x + 5 ) ( x - 4 ) for f x in the equation y = f ( x ) - 3 yields y = ( x + 6 ) ( x + 5 ) ( x - 4 ) - 3 . Substituting - 6 for x in this equation yields y = ( - 6 + 6 ) ( - 6 + 5 ) ( - 6 - 4 ) - 3 , or y = - 3 . Substituting - 5 for x in the equation y = ( x + 6 ) ( x + 5 ) ( x - 4 ) - 3 yields y = ( - 5 + 6 ) ( - 5 + 5 ) ( - 5 - 4 ) - 3 , or y = - 3 . Substituting 4 for x in the equation y = ( x + 6 ) ( x + 5 ) ( x - 4 ) - 3 yields y = ( 4 + 6 ) ( 4 + 5 ) ( 4 - 4 ) - 3 , or y = - 3 . Therefore, when x = - 6 then y = - 3 , when x = - 5 then y = - 3 , and when x = 4 then y = - 3 . Thus, the table of values in choice B represents y = f ( x ) - 3 . Choice A is incorrect. This table represents y = x - 3 rather than y = f ( x ) - 3 . Choice C is incorrect. This table represents y = x + 3 rather than y = f ( x ) - 3 . Choice D is incorrect. This table represents y = f x + 3 rather than y = f ( x ) - 3 .

$x$	$y$
$negative 6$	$negative 9$
$negative 5$	$negative 8$
$4$	$1$

$x$	$y$
$negative 6$	$negative 3$
$negative 5$	$negative 3$
$4$	$negative 3$

$x$	$y$
$negative 6$	$negative 3$
$negative 5$	$negative 2$
$4$	$7$

$x$	$y$
$negative 6$	$3$
$negative 5$	$3$
$4$	$3$

Question 91bb6f