Exponential functions
A graph of the function y = ax is an exponential function.
y = ax meets the y-axis (thus creating the y-intercept) at y = a0 = 1. So (0, 1) is the y-intercept.
For large ,
, and
for small x, ,
but does not touch the x-axis.
This function can be represented graphically as below:
And the domain and range for the function are:
Domain : {all real x}
Range : {y : y > 0}
Logarithmic functions
Logarithmic functions are inverse functions of exponential functions. They are given by:
y = f(x) = , where a is the base, which means ay = x
Now the x intercept for f(x) = y = is
0 =
x = a0 = 1
So (1, 0) is the x-intercept point.
The logarithmic function can be represented graphically below:
Domain : {x : x > 0}
Range : {all real y}
To get the different data points for this function, use the ‘log’ key on your calculator and complete the table for log x
x | -2 | -1 | 0 | 0.5 | 1 | 2 | 3 | 4 |
y | * | * | * | -0.3 | 0 | 0.3 | 0.5 | 0.6 |
* means values don’t exist