Graph this function using graphing algorithm.

y=x²/(x²+1)

use the function and find :
x and y intercept
and assymptotes

use the first derivative and find:
critical points.

use the second derivative and find:
concavity
and points of inflection.

Hello rafie !

Y =  x^2 / (x^2 + 1)

Y = (x^2 + 1 - 1)/(x^2 + 1)

Y = 1 - 1/(x^2+1)

1)It is clear that the function is always less than 1

2) x = 0  --> y = 0

3) when x is equal to infinty then y = 1.

4) dy/dx = 2x/(x^2+1)^2 i.e  x>0  increasing  and x < 0 decreasing ...

Now the graph is simple ...

Both side ...symmetric ..

Regards

Yagya

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