exponential and logarithmic functions
MHF4U: Advanced Functions
Exponential Functions and Their Inverses
J. Garvin
Slide 1/15
exponential and logarithmic functions
Exponential Functions
A basic exponential function, without transformations applied
to it, has the form y=bx, where bis the base.
If b>1, the function is called an exponential growth
function.
As xincreases, yincreases rapidly.
J. Garvin — Exponential Functions and Their Inverses
Slide 2/15
exponential and logarithmic functions
Inverse of an Exponential Function
A graph of y= 2xis below. Note, for example, that when
x= 2, y= 22= 4, and that when x=−1, y= 2−1=1
2.
J. Garvin — Exponential Functions and Their Inverses
Slide 3/15
exponential and logarithmic functions
Exponential Functions
An exponential function has a repeating pattern in its finite
differences.
x f (x)=2x∆1 ∆2 ∆3
0 1
1 2 1
2 4 2 1
3 8 4 2 1
4 16 8 4 2
5 32 16 8 4
The base of the function is the ratio between any two terms
in the finite differences.
J. Garvin — Exponential Functions and Their Inverses
Slide 4/15
exponential and logarithmic functions
Inverse of an Exponential Function
Recall that a function and its inverse are related by switching
the independent and dependent variables.
For example, the inverse of the function y= 2xis x= 2y.
This inverse relation can be graphed either by choosing
values for yand substituting them into the equation.
J. Garvin — Exponential Functions and Their Inverses
Slide 5/15
exponential and logarithmic functions
Inverse of an Exponential Function
A graph of x= 2yis below. Note, for example, that when
y= 2, x= 22= 4, and that when y=−1, x= 2−1=1
2.
J. Garvin — Exponential Functions and Their Inverses
Slide 6/15
