Give an example of an exponential function that has a range (3,infinity)
y=3* 10^x for x>=0
To find an exponential function with the given range, we need to find a suitable base and coefficient.
One possible example is the function f(x) = 3 * 2^x.
To verify that this function satisfies the given range, let's evaluate f(x) for different values of x.
When x = 0, f(0) = 3 * 2^0 = 3 * 1 = 3.
As x increases, the exponential term 2^x will also increase, resulting in f(x) growing exponentially. Therefore, for any value of x greater than 0, f(x) will be greater than 3.
Hence, the range of this function is (3, infinity), since it includes all values greater than 3.
By adjusting the coefficient (in this case, 3) and the base (in this case, 2), you can create various exponential functions with different ranges.