Sunshine Maths

Exponential functions

A graph of the function y = a^x is an exponential function.

y = a^x 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 are inverse functions of exponential functions. They are given by:

y = f(x) = log_a x , where a is the base, which means a^y = 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