Question

Help with graphing the following?

Answer 1

\(\ \huge \color{blue} y \color{blue}=\color{blue}2 \color{green}+\frac{1}{x+1} \).

Answer 2

first identify vertical and horizontal asymptotes
vertical:
- set denominator to 0
horizontal:
- if degree on bottom is bigger, then asymptote is y=0
- add 2 for vertical shift

Answer 3

that is the inverse function shifted 2 up and 1 left

Answer 4

What's the inverse function? @dumbcow How do I know that this function contains an asymptote?

Answer 5

if there is an x-value that makes the function undefined then it has a vertical asymptote.
- set denominator =0, if solution exists....theres an asymptote

Answer 6

Set x=0 or the entire denominator=0?

Answer 7

the inverse function is :
y = 1/x

Answer 8

entire denominator.....x+1 = 0

Answer 9

Now I get it. So The 2 means to shift it up by 2, and The x+1 indicates a horizontal shift to the right 1?

Answer 10

I take the y=x graph and apply the above transformations? To both?

Answer 11

almost...it will be a shift to left
x+1 = 0
x = -1 --> this line is your asymptote

Answer 12

So how would I find the y asymptote?

Answer 13

there are 3 rules for rational functions:

higher exponent on top --> No asymptote
Same exponent --> y = ratio of leading coefficients
higher exponent on bottom --> y=0

so for this example, as x -> infinity, y->2+0 or just 2