Question

How can you distinguish between linear and exponential functions? How do linear and exponential functions compare as the domain increases?

Answer 1

On a function f(x), as the domain increases, x increases or becomes more positive.

A linear function is one where the dependent variable has a power of one, such as

x
2x
.5x

All of those x are raised to power of one.

Exponential functions have x raised to different powers such as 2, 3, 4, 5.
Exponential functions increase much faster than linear functions as the domain increases. The derivative of an exponential is larger than linear function in most domains.

Answer 2

linear functions have a constant slope
exponential don't, they either increase rapidly or decerse rapidly

as the domain increases, linear functions aproach positive or negative infinity at a constant rate
as the domain increases, exponential function apporoaches positive or negative infinity, but usually much faster than a similar linear function