GRAPHS ON THE GO: GIF effect -3

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Here we are back with the finale of GIF effect.

This time we will monitor the effect of GIF when it is applied to x only.

We better take the same example which we have been taking since the last two parts which is y = sinx.
Hence we have to work on the following transformation.
y     =     sin x         (original)
y     =     sin[x]       (modified)

Lets analyse what should happen-
that how GIF works.
Keeping in mind the same concept we will proceed-
As the the GIF is applied to x hence the sine function will get an integer input every time and accordingly we will get the values of y.
π/2
interval of x                 input in sine function                    output(y)
.from -infinity
.
.
.
.
x∊[-1,0)                                  -1                                            -sin(1)
x∊[0,1)                                    0                                               0
x∊[1,2)                                    1                                             sin(1)
x∊[2,3)                                    2                                             sin(2)
x∊[3,4)                                    3                                             sin(3)
.
.
.
.
...so on.

Hence at each integral value of x the graph will break and remain constant with the same value uptill the next integer comes. as the y is a sine function hence its value will never shoot beyond 1 and below -1.

Now let's see their graphs-


Original Graph


Modified graph
 As predicted the results are similar.

#Summary-
Step 1: Find the points where the function breaks.
Step 2: Find the final input into the base function(here sine).
Step 3: Generalise the observation.

A quick glimpse-





(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




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