Question

How do you graph `y = 1/(1 + x^2)`?

Answer 1

See explanantion

Explanation:

As you have `x^2` then `1+x^2` will always be positive. So `y` is always positive.

As `x` becomes smaller and smaller then `1/(1+x^2) -> 1/1 = 1`

So `lim_(x->0) 1/(1+x^2)=1`

As `x` becomes bigger and bigger then `1+x^2` becomes bigger so `1/(1+x^2)` becomes smaller.

`lim_(x->+-oo) 1/(1+x^2)=0`

`color(blue)("build a table of value for different values of "x" and calculate the appropriate values of y. Plot")` `color(blue)(" the obtained values of y against those chosen for x")`