I saw two different forms for an exponential function which are:
- $f(x)=a^x$
and
- $f(x)=a \cdot b^x$ where $a$ is the initial value
Are the rules and cases the same in both forms such as:
- It is always greater than 0, and never crosses the x-axis
- It always intersects the y-axis at y=1 ... in other words it passes through (0,1)
- At x=1, f(x)=a ... in other words it passes through (1,a)
- It is an Injective (one-to-one) function
- Its Range is the Positive Real Numbers: (0, +∞)
and so on.