TITLE: Sketching weird Exponential graph
QUESTION [6 upvotes]: The formula of the line is -
$$ y = 1 + 2^{-x} $$
Sketch the graph and show clearly whether it passes through the point $ (1,1) $
When $X = 0$ , 
$y =2$, so the $y$ intercept is at $y = 2$ .
When $X = 1$, 
$Y = 1.5$ , this shows that it does not pass through the point $(1,1)$ 
When $X = 3$ , 
$Y = 1.125$. 
However when $X = 1000, 10000,100000$ 
All $Y$ values is $1$, 
So how do I go about sketching this graph ? I'm a little confuse . Thanks for the help !

REPLY [5 votes]: Test out a few points. You'll see as x approaches infinity, y approaches 1. As for the other side of the graph, you can see that it just continues increasing, getting very steep very quickly. Here is small section of the graph: