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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 {x}~right~infty{a^x}~right~infty, and

for small x, {x}~right~-infty{a^x}~right~0 but does not touch the x-axis.

This function can be represented graphically as below:

exponential function

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) = log_a x, where a is the base, which means ay  =  x

Now the x intercept for f(x) = y = log_a x is

0  =  log_a x    doubleright  x = a0  =  1

So (1, 0) is the x-intercept point.

The logarithmic function can be represented graphically below:

logarithmic function

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