what is the different of exponents functions?

Answer 1

Moreover, 'exponential functions', have a horizontal asymptote; a value below or above which they do not cross. It is usually the 'c' term of the expression y = 3^x (c = 0) hence, it's horizontal assymptote is 0 (does not go below 0).

y = 3^x - 3 (horz asymptote = -3)

If 'x' is negative, y = 3^(-x), the function behaves as so: y = 1/3^x (hence, instead of increasing, it starts off at infinity and then goes near to 0 (range)).

If y = -3^x
Then it would not be a function as it does not exist for certain values of 'x' (not continuous). It actually looks somewhat like a trig function if you did connect the dots. This one would be diverging (from 0).
If y = -.04^x, it would be converging (at 0), but still not a function.

Actually, really easy stuff if you just graph it on a calculator, or try to make a table for each example and then attempt to graph it manually.

Answer 2

Just to clarify, exponential functions don't **always** have to be based on e. The natural logarithm and 'natural growth' number come up so often that when one says 'exponential function' that's what everyone thinks. But 10 (the base of the common logarithm system) can also be used. In fact a^(x) where a and x are any numbers > 0 is an 'exponential' function.


Doug

Answer 3

exponent functions are different from normal functions as they have no limiting boundaries.
e^x,e^-x are examples of exponential functions
where e equals approximately 2.71828183 and is the base of the natural logarithm.