Question

What is the range of this exponential function?

Answer 1

To determine the range of an exponential function, we need to find the set of all possible output values or y-values. The range of an exponential function of the form y = ab^x, where a and b are real constants, depends on the value of b.

If b is greater than 1 (b > 1), the graph of the exponential function is increasing. This means that the range is given by all positive numbers greater than 0 (y > 0).

If 0 < b < 1 (0 < b < 1), the graph of the exponential function is decreasing. This means that the range is given by all positive numbers less than 1 (0 < y < 1).

If b = 1, the graph of the exponential function is a horizontal line at y = a. This means that the range is a single-point set {a}.

Therefore, without the specific equation of the exponential function, we cannot determine the exact range of the function. Additional information is needed.