a Function f is defined as f(x)=3*2^x

a)is f increasing or decreasing?
b)write equation for the horizontal asymptote
c)describe the end behavior of

a)f'(x)=3*ln(2)*2^x>0

b)y=0 (limf(x)=0 if x--> -inf)
c)?

please explain your b and a.

a)If f'(x)>0 then f(x) is increasing

b)x | f(x)
0 | 3
-1 | 3/2
-2 | 3/4
-3 | 3/8
-10 | 3/1,024
-20 | 3/1,048,576
-30 | 3/1,073,741,824
-33 | 3/8,589,934,592

To determine whether the function f(x) = 3 * 2^x is increasing or decreasing, we need to examine its derivative. The derivative of a function indicates whether it is increasing or decreasing at any given point.

To find the derivative of f(x), we can use the rules of differentiation. The derivative of 2^x is found using chain rule: d/dx(2^x) = (ln(2) * 2^x). Therefore, the derivative of f(x) = 3 * 2^x is f'(x) = (ln(2) * 3 * 2^x).

a) The function f(x) = 3 * 2^x is increasing. We can verify this by noting that the derivative f'(x) = (ln(2) * 3 * 2^x) is always positive, since ln(2) and 3 are positive constants, and 2^x is always positive for any real value of x.

b) To determine the equation for the horizontal asymptote, we need to examine the behavior of the function as x approaches positive or negative infinity.

As x approaches positive infinity, the term (2^x) will become increasingly large, resulting in f(x) also becoming larger. Therefore, there is no horizontal asymptote for the function f(x) = 3 * 2^x.

c) The end behavior of the function f(x) = 3 * 2^x as x approaches positive or negative infinity is that it increases without bound. This means that as x becomes very large (positive or negative), the function values of f(x) also become very large (positive).

In summary:
a) The function f(x) = 3 * 2^x is increasing.
b) There is no horizontal asymptote for the function f(x) = 3 * 2^x.
c) The end behavior of the function f(x) = 3 * 2^x is that it increases without bound as x approaches positive or negative infinity.