Dear Learner,

I hope you find the lesson clear and engaging, with easy-to-follow demonstrations. You’ll discover the main points of the lesson presented in bullet points. Enjoy your reading!

• A function from  set A to set B  is a relation from A to B with the condition that for every element in the domain, there exists a unique(only one) image in set B.
• A relation R is a function if and only if any vertical line intersects graph of R only once.
• a function which can be written in the form of$f(x) = ax^{r}$, where $ a, r \in \mathbb{R}$.
• the absolute value of a real number a denoted by $|a|$ is anon negative real number defined by$|a| = \begin{cases}\ a &\text{if} a \ge 0,\\ -a & \text{if} a<0, \end{cases}$
• the function defined by $f(x)$ = |x| = $\begin{cases}\ x & \text{if } x \ge 0, \\ -x & \text{if } x < 0. \end{cases}$
• the function defined by $f(x)$ =sgn x = $\begin{cases}\ 1 & \text{if} x >0, \\ 0 & \text{if} x = 0, \\ -1 & \text{if} x < 0,\end{cases}$ is the signum function.
• the function defined by $f(x) = \lfloor x \rfloor $ is the largest integer lessthan or equal to x is called the floor function.