Question 1076155
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>>The graph below:<< 
`
{{{drawing(400,400,-4,10,-7,7,
green(line(3,-20,3,20)),circle(4,2,.15),locate(4.15,2.3,"(4,2)"),
circle(4,2,.1),

graph(400,400,-4,10,-7,7,2/(x-3)) )}}}
`
>>has a vertical asymptote at x=3,<< 
<pre>
So it could have a denominator that when set = 0, gives

x=3,

So its denominator could be x-3.  So the equation could

be like this:   {{{y="?"/(x-3)}}}
</pre>
>>a horizontal asymptote at y=0,<< 
<pre>
That means its numerator would have to be of less degree than 
its denominator.  So if its denominator is x-3, which is of 
degree 1, then its numerator would have to be of degree 0, 
which would be a constant, say, k.  Then the equation could

be like this:   {{{y="k"/(x-3)}}}
</pre>
>>and passes through the point (4,2). 
what could be the function of this graph?<<
<pre>
We substitute x=4 and y=2 into

{{{y="k"/(x-3)}}}

{{{2="k"/(4-3)}}}

{{{2="k"/1}}}

{{{2=k}}}

So substituting k=2, the equation could be this function:

{{{y= 2/(x-3)}}}

or if we use function notation:

{{{"f(x)"= 2/(x-3)}}}

Edwin</pre><b></font>