Question 825669
Graph the rational equation {{{"f(x)"}}}{{{""=""}}}{{{(x^2-25)/(x-5)}}}

{{{drawing(400,400,-8,8,-3,13,graph(400,400,-8,8,-3,13),
line(-22,-17,4.8,9.8),line(5.15,10.15,20,25), circle(5,10,.2) )}}}

a. What do you notice about the graph at x = 5?
<pre>
The equation is undefined at x=5, as {{{cross(0/0)}}} is not defined.

{{{cross("f(5)"=(5^2-25)/(5-5)=(25-25)/(5-5)=0/0)}}}

That's why there is a hole in the graph, indicated by the
open circle.
</pre>
b.	Use the graph to estimate the limit as x approaches 5.
<pre>
We can see that as x approaches 5 the value of y approaches 10, and we
write {{{matrix(2,1,lim,"x->5")}}}{{{((x^2-25)/(x-5))}}}{{{""=""}}}{{{10}}}. 
</pre>
c.	What do you think is the correlation between a graph and a limit?
<pre>
That's a very vague question.  I'm guessing that what it's asking is that for
the graph of f(x) to be continuous at x=a, this must be true

{{{matrix(2,1,lim,"x->a")}}}{{{("f(x)")}}}{{{""=""}}}{{{"f(a)"}}}.

Edwin</pre>