# Home > Introduction to Pre-Calculus > Introduction to Graphing Functions > Exponential and logarithmic functions

# Exponential and logarithmic functions

## 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