Answer:
Option C is correct.
[tex]f(x)=-3(6)^{x+2}[/tex]
Explanation:
The exponential function is of the form:
[tex]f(x) = ab^x[/tex] where a is constant and b is the base.
*If base b>1
(i) For positive value of a.
If x increases then, f(x) tends to positive infinity.
(ii)For negative value of a.
if x increases, then f(x) tends to negative infinity.
*if 0<b<1 ,
(i)For positive value of a.
If x increases then, f(x) tends to 0.
(ii)For negative value of a.
if x increases, then f(x) tends to 0.
Then from the given options
The only function [tex]f(x)=-3(6)^{x+2}[/tex] ; where a = -3 <0 and b=6>1 is decreasing and approaches negative infinity as x increases .
