## Thursday, August 21, 2014

### Even and odd functions

A function is even if f(−x)=f(x) for all values of x.
A function is odd if f(−x)=−f(x) for all values of x.
The graph of an even function is symmetric with respect to the y-axis.
The graph of an odd function has rotational symmetry with respect to the origin, meaning that its graph remains unchanged after rotation of 180 degrees about the origin

From http://www.asic-world.com/digital/intro1.html#Numerical_Presentation

http://nptel.ac.in/courses/Webcourse-contents/IIT-%20Guwahati/digital_circuit/frame/index.html

## Wednesday, August 20, 2014

### Changing the base of logs in Maxima

From http://math-blog.com/2007/06/04/a-10-minute-tutorial-for-solving-math-problems-with-maxima/,  you can change the base of logs by using the formula below. Log in Maxima is to the base of e. Changing to the log of base 10 is as follows -

log10(x):= log(x)/log(10);

So for logs to the base 9, below is what you should be using for the software

log9(x):= log(x)/log(9.0);

For example,

log9(x):= log(x)/log(9.0);
log9(81.0);

which should give an answer of 2.0. I had to use a decimal point for most of the  numbers in the brackets.

### Number of solutions to linear equations

When x= some number then you have a solution.
If you get something like 5=7 then you have no solution.
If both sides are equal like 3x+5 = 3x+5 then you have infinite number of solutions.

## Tuesday, August 19, 2014

### Recognizing rational and irrational expressions

The sum, difference, product or quotient of two irrational numbers could be either rational or irrational. Therefore, the other expressions could be either rational or irrational, as we see below.

If c=2 and d=21, then cd=1 is rational.
If c=2 and d=2, then cd=22 is irrational.
If c=22 and d=2, then

c/d=2
is rational.
If c=2 and d=24, then cd=24 is irrational.