GRAPHS ON THE GO: GIF effect - 2

Here we are back again with GIF (Greatest Integer Function) effect, this time we will learn its effect when it is applied to y.

In case you still do not know the work of GIF, you should visit-

point 9 @ http://feed-o-math.blogspot.com/2020/05/graphs-on-go-introduction.html

Let's begin....

Like always lets take an example-

y     =     sinx        (original)

[y]  =     sinx        (modified)

 

Lets analyse what effects should appear when this kind of transformation is done by using our basic knowledge of GIF.

We have-

[y]  =  sinx 

You should be very clear up till this point that LHS will come out to be an integer.

Now this means that sinx will always be equal to an integer in this case.

And it is well known that sinx takes up values from -1 to 1 inclusive.

which further means x will be-

nπ                           for                sinx = 0         and               [y] = 0

2nπ + (π/2)             for                sinx = 1         and               [y] = 1

2nπ + (3π/2)           for                sinx = -1        and               [y] = -1

Now we need to understand that for what values of y will the [y] = 0 , 1, -1.

After knowing this we can easily extract the graph required.

for-

y ε [0,1)                  [y] = 0

y ε [1,2)                  [y] = 1

y ε [-1,0)                 [y] = -1

After knowing all these technicalities we can easily plot the graph

Now lets the original and modified graph-

Original Graph

Raw modified graph
Just remove the black base graph of sinx
and you get the modified graph

In this way application of [y] transforms the graph.

#Shortcut to make this kind of graph transformation

Step 1: Draw the base graph.

Step 2: Mark the point where y is integer.

Step 3: Analyse intervals for that particular integer and extend the point accordingly

            Example-

                            if y = 1, then for [1,2)          y = 1

                            if y= -1, then for [-1,0)        y = -1

Note- Do not forget to exclude unwanted points.

Step 4: Remove the base graph.

    

Boom 

You are done.

Lets take quick glimpse of the 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