x g x - 1 25 0 1 1 1 25 2 1 625 For the exponential function g ,

Question

x g x - 1 25 0 1 1 1 25 2 1 625 For the exponential function g , the table shows four values of x and their corresponding values of g x . Which equation defines g ?

Accepted Answer

Choice D is correct. It's given that function g is exponential. Therefore, an equation defining g can be written in the form g x = a b x , where a and b are constants. The table shows that when x = 0 , g x = 1 . Substituting 0 for x and 1 for g x in the equation g x = a b x yields 1 = a b 0 , which is equivalent to 1 = a . Substituting 1 for a in the equation g x = a b x yields g x = b x . The table also shows that when x = 1 , g x = 1 25 . Substituting 1 for x and 1 25 for g x in the equation g x = b x yields 1 25 = b 1 , which is equivalent to 1 25 = b . Substituting 1 25 for b in the equation g x = b x yields g x = 1 25 x . Choice A is incorrect. For this function, g 1 is equal to - 25 , not 1 25 . Choice B is incorrect. For this function, g 1 is equal to - 1 25 , not 1 25 . Choice C is incorrect. For this function, g 1 is equal to 25 , not 1 25 .

$x$	$g (x)$
$negative 1$	$25$
$0$	$1$
$1$	$\frac{1}{25}$
$2$	$StartFraction 1 Over 625 EndFraction$

Question f9da1b