**Question:** What is the domain of an
exponential function f(x) = kb^{x}? What is the range?
Describe the shape of the graph for b > 1, and for b < 1. What happens
to f(x) in each case when x becomes very large (increases without bound)
and as x becomes very small (decreases without bound)? Are there any
horizontal asymtotes?
**Answer:** The domain of an exponential function of
this form is **all real numbers**. The range (co-domain) is all
**positive real numbers**.

For b > 1, f(x) is increasing -- its graph **rises **to the right.
As x increases without bound, so does f(x), but as x decreases without
bound, f(x) approaches zero. The line y = 0 (the x-axis) is a
horizontal asymptote.

For b < 1, f(x) is decreasing -- its graph **falls** to the right.
As x increases without bound, f(x) approaches zero, so the x-axis is a
horizontal asymptote. On the other hand, as x decreases without bound,
f(x) grows infinitely large. The left end goes up and the right end
slides along the x-axis.