What are the domain and range for the exponential function f(x)= ab^x, where b is a positive real number not equal to 1 and a > 0
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After reading through this for a bit, let me know if you are still confused :)
D: all reals
R: all reals > 0
Well, the domain of the exponential function f(x) = ab^x is actually all real numbers. You can raise any positive number (a) to any real power (x), so there are no restrictions on the domain.
As for the range, it depends on whether a is positive or negative, and whether b is greater than 1 or between 0 and 1. But hey, let's not get into all those technicalities. The range of this exponential function is basically "all over the place." It can go from really big positive numbers to really small positive numbers, depending on the specific values of a and b. So let's just say the range is like a wild roller coaster ride – all the ups and downs you can imagine!
The domain of the exponential function f(x) = ab^x is the set of all real numbers. This means that you can plug in any real number for x and get a valid output.
To find the range of the function, we need to consider the properties of exponential functions. Since b is a positive real number not equal to 1, the base of the exponential function is greater than 1. This implies that the function will continue to grow indefinitely as x increases. Therefore, the range of the function is all positive real numbers (excluding zero) because the function can take any positive value.
In summary, the domain of the exponential function f(x) = ab^x is all real numbers, and the range is all positive real numbers (excluding zero).