GRAPHS ON THE GO: GIF effect -3
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-
As we know from point 9 @ http://feed-o-math.blogspot.com/2020/05/graphs-on-go-introduction.html
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.
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