Question 9 ( 2 points) Given the exponential function $y=-4\left(3^{x}\right)+2$ state the range A

Step 1 ：The range of a function is the set of all possible output values (y-values) that we get when we input all possible x-values into the function.

Step 2 ：For the given function \(y=-4\left(3^{x}\right)+2\), as x approaches infinity, \(3^x\) also approaches infinity. However, because of the negative sign in front of the \(4(3^x)\), as x approaches infinity, \(-4(3^x)\) approaches negative infinity. Adding 2 to a number that is approaching negative infinity will still approach negative infinity.

Step 3 ：On the other hand, as x approaches negative infinity, \(3^x\) approaches 0. Therefore, \(-4(3^x)\) approaches 0, and adding 2 to a number that is approaching 0 will approach 2.

Step 4 ：Therefore, the range of the function is \((-\infty, 2]\).

Step 5 ：\(\boxed{The range of the function is (-\infty, 2]}\)