Exponential Function Reference
This is the Exponential Function:
f(x) = ax
a is any value greater than 0
Properties depend on value of "a"
- When a=1, the graph is a horizontal line at y=1
- Apart from that there are two cases to look at:
Plot the graph here (use the "a" slider)
- 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 Domain is the Real Numbers:
Its Range is the Positive Real Numbers: (0, +∞)
So the Exponential Function can be "reversed" by the Logarithmic Function.
The Natural Exponential Function
This is the "Natural" Exponential Function:
f(x) = ex
Where e is "Eulers Number" = 2.718281828459... etc
Graph of f(x) = ex
At the point (1,e) the slope of the line is e and the line is tangent to the curve.