Question

Find the range of the exponential function f(x) = 3(1/2)x

Answer 1

 f(x) = 3(1/2)x is not properly formed; if you meant exponentiation here, please write the function as

f(x) =  f(x) = 3(1/2)^x.

The range is the set of all possible values of y (that is, all possible values of f(x).  Try out a few x values and see what you get:

f(-5) = 3(1/2)^5   (note that this is positive)

f(0) = 3(1/2)^0 = 3 (this is positive)

f(4) = 3(1/2)^4 = 3/16 (this is positive)

There is no x value for which f is negative, and none for which f is 0.  Given this info, what do YOU think the range of    f(x) = 3(1/2)^x is?

Write it in the form   (a,b).