Question 1206248
<pre>
We want a graph like this. 

{{{graph(200,200,-3,3,-3,3, -e^(x)+1,sqrt(sin(9x))/sqrt(sin(9x))))}}}

One that goes through the origin to have a y=intercept of 0. 
It must go up, as close to 1 as possible, but never quite to 1,
because it has a range of y < 1, so it has a horizontal asymptote at y=1

How do we get an equation for a graph to look like that?

We start with the basic exponential equation.
{{{y=e^x}}}. It has a range of x > 0, and horizontal asymptote y=0,
which is the x-axis

{{{graph(200,200,-3,3,-3,3, e^x)}}}
We want to get it below the x-axis, so we reflect it in the x-axis by
multiplying the right side by -1
{{{y=-e^x}}}

{{{graph(200,200,-3,3,-3,3, -e^x)}}}


Now all we need to do is shift the graph and its horizontal asymptote
2 units upward, by adding +1 to the right side. That will take care of
both raising the asymptote from y=0 to y=1 and the y-intercept of -1 up to 0.
{{{y=-e^x+1}}}

{{{graph(200,200,-3,3,-3,3, -e^(x)+1,sqrt(sin(9x))/sqrt(sin(9x))))}}}

Its domain is {{{(matrix(1,3,-infinity,",",infinity))}}}

Its horizontal asymptote is {{{y=1}}}

Its x-intercept (and its y-intercept) is (0,0). 

Edwin</pre>