Question

What are the asymptotes of `y=-1/(x+4)+3` and how do you graph the function?

Answer 1

`y` = `-1/(x+4) + 3` = `(3x +11)/(x+4)`

• Asymptote of y : x = -4
• Asymptote of x : `lim_(x->∞)` `(3x +11)/(x+4)` = `3`
• Intersection x axis : y = 0 `->` `-11/3` = `-3.67`
• Intersection y axis : x = 0 `->` `11/4` = `0.275`
• Graph :

graph{-1/(x+4) + 3 [-16.39, 16.39, -8.19, 8.19]}