Things that I learnt today. Emphasis on the I, I couldn’t make for MAM1000W today.

• Absolute value definition
• Properties of absolute values
• Rules for inequalities

Absolute value

The absolute value of a number represents the distance between that number and \(0\) on the real number line. Absolute value of a number \(n\) is denoted by \(|n|\) which is equal to \(\sqrt{n^{2}}\) which is from the distance formula. Since it is the distance between \(0\) and \(n\) Hence \(|n|=n\) if \(n \geq 0\) and \(|n|=-n\) if \(n < 0\)

Properties of Absolute values

1. \(|nm| = |n||m|\)
2. \(|\frac{n}{m}| = \frac{|n|}{|m|}, (m \neq 0)\)
3. \(|n^{m}| = |n|^{m}\)

Let \(n > 0\) then

1. \(|m| = n \iff m = \pm{n}\)
2. \(|m| < n \iff -n < m < n\)
3. \(|m| > n \iff m > n, m < -n\)

Rules for inequalities

1. if \(n<m\) then \(n+p<m+p\)
2. if \(n<m\) and \(p<q\) then \(n+p<m+q\)
3. if \(n<m\) and \(p>0\) then \(np<mp\)
4. if \(n<m\) and \(p<0\) then \(np>mp\)
5. if \(0<n<m\) then \(\frac{1}{n}>\frac{1}{m}\)

So today we basically learnt about different ways to represent a function and we defined what a function is in detail.

First things first, what is a function?

A function is a rule that assigns each element x ( x being any independent variable ) in a set A exactly one element, f(x) ( f(x) being a dependent variable ) in a set B.

From that definition of a function we can now distinguish the different types of ways to represent a function.

I only know four ways, maybe there’s more… idk

1. algebraically, with the use of an equation
2. graphs
3. tables
4. or just in words

So we also learnt how to test if a graph represents a function. To do that you have to use the vertical line test. which means that anywhere within the domain of the graph if an x value has more than one f(x) value assigned to it then that graph does not represent a function.…