Function sketching

Question

sketch the graph y= 1+ 3x divides by x squared + 2

Answer 1

I assume that you have a rational algebraic function, and that your word 'divides' should have been divided.

 

If, specifically, y = [1+3x] / [x²+2] then this graph has an horizontal asymptote, y = 0. It has no vertical asymptote.

 

The y-intercept is (0, ½).

 

The x-intercept is (-1/3, 0). On the interval (-infinity, -1/3) the y values are always negative; elsewhere the y values are always positive.

 

I assume you can sketch this, now, with special attention to END BEHAVIOR.