Question

Graph the rational function y=x/x^2+2x+1. Both branches of the rational function pass through which quadrant?

Answer 1

See attachment and explanation below. (3rd Quadrant)

Explanation:

After graphing the rational function, it is to notice that branches occurs at values where discontinuities exist. Besides, it is evident that branchs pass through the 3rd Quadrant. (x, y < 0)

Answer 2

Quadrant 3

Explanation:

Here we have to graph the function y = x/(x^2 + 2x + 1)

The denominator can be factored.

x^2 + 2x + 1 = (x + 1)(x + 1)

y = x/(x + 1)(x + 1)

Now we have to graph this function and see in which quadrant the function's both branches passes through.

Herewith I have attached the graph.

Here we can see both branches pass through Quadrant 3.

I hope this will helpful.

Thank you.