GRAPHS ON THE GO: GIF effect - 1

In this post we are going to learn about the effect of Greatest Integer Function(GIF) when applied to a function.

Hope you all know the working of GIF , in case you are unaware of its working, visit point 9 of-

http://feed-o-math.blogspot.com/2020/05/graphs-on-go-introduction.html

Always remember in order to perform graphical transformations you need know the basic working of the function which is applied to a function to transform it.

For this kind of transformation you need to know the graph of the function to which GIF is applied in order to get precise results.

So lets begin with an example-

y =  sinx         (original)

y = [sinx]       (modified)

Now lets see what effect occurs on the graph due to this.

The original graph looks like this-

                                    

After application of GIF, in order to draw the graph we will break down the input(sinx) in GIF into different sections-

Case 1. For 0< sinx < 1

Case 2. For sinx = 1 , 0 , -1 (The points at which input takes integer values.)

Case 3. For -1 < sinx < 0

Now we know that if input inside GIF is not an integer it returns the value equal to nearest integer less than the input.

Now the different section will return the new values of  y which are as follows-

Case 1. y = 0

Case 2. y = 1 , 0 , -1 (As GIF does not have any effect on an integer)

Case 3. y = -1

Now we will replace the values accordingly and will plot a new graph which is as follows-

Just a quick glimpse-

Hope now you will be able to know the process of doing this kind of transformation.

(Image credits- https://www.desmos.com/)

Stay Tuned for the next post.

For any query comment down there.

#graphs_on_the_go  #understanding_graphs #mathematics, #feed-o-math , #quadratic_equations