# Sketching weird Exponential graph

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 !

• When $x$ = 1000, $y$ does not equal 1, it equals 1.0000...0000something. There are so many 0's between the 1 and the something, that your calculator can't print them. So the $y$ corresponding to this $x$ is just a few atoms above the line whose equation is $y=1$. Your pen is much too wide for you to distinguish between the graph you are trying to draw and this line.
– MasB
Sep 22, 2016 at 16:16

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: 