The exponential function

The exponential function is the function

Properties:

1. 
2. 
3. 
4. 

the exponential function is bijective and invertible

If $a, b\in(0,+\infty) \text{ and } x, y\in \mathbb{R}$, then:

1. 2. 3.

4. 5.

Try it

The exponential function, with the base a on a slider.

The chapter states that the function is strictly increasing when a > 1 and strictly decreasing when 0 < a < 1. Drag a through 1 and watch the curve turn over. At exactly a = 1 it flattens into the constant line y = 1, which is why the definition excludes it.

Whatever a is, the curve passes through (0, 1) and never touches the x-axis.