Question 988860
<pre>
The other tutor thought you only said "a range of -2" because you used < without
skipping a space after it.  Of course you did not know not to do that.  This
site uses HTML and when you type anything after the symbol < without skipping a
space after it, the HTML thinks it's an HTML tag and doesn't print it. So
hereafter, if you submit a problem that involves the symbol " < ", always skip a
space after it, so what comes after it will not be deleted. 

I looked to see what you had typed and was able to answer your question.
What you typed was this:</pre>Draw the graph of a function p that fits the following description: p has a domain of 
all real numbers and a range of -2< y &#8804; 5, p(-1)=p(4), and p is discontinuous at x=2.<pre>
This would be a piecewise function.  Here is an equation of such a function:

{{{p(x)=system(

matrix(2,3, (6-2x^2)/(x^2+1),for, x<2, 1.5, for,x>=2))}}}

You weren't asked for the equation but only the graph.  But this is the
equation for such a function p(x)

Here's its graph, and its explanation below the graph:

{{{drawing(400,400,-6,6,-5,7,circle(2,-.6,.13),
red(line(2,1.5,20,1.5)),
green(line(-20,-2,20,-2)),

circle(-1,1.5,0.09),circle(-1,1.5,0.07),circle(-1,1.5,0.05),circle(-1,1.5,0.03),circle(-1,1.5,0.01),

circle(2,1.5,0.15),circle(2,1.5,0.13),circle(2,1.5,0.11),circle(2,1.5,0.09),circle(2,1.5,0.07),circle(2,1.5,0.05),circle(2,1.5,0.03),circle(2,1.5,0.01),

circle(4,1.5,0.09),circle(4,1.5,0.07),circle(4,1.5,0.05),circle(4,1.5,0.03),circle(4,1.5,0.01),









graph(400,400,-6,6,-5,7, 



((5-2x^2)/(x^2+1))*(sqrt(1.95-x)/sqrt(1.95-x) )) )}}}

Notice that its domain is all real numbers, because there is no value of
x for which we cannot find a value for p(x).  Notice that the graph approaches
the green line y = -2 on the left as a horizontal asymptote, which means the
graph never quite gets as low as -2 but it does reach 5 at x=0, so its range is
-2 < y &#8804; 5.  The graph goes only as high as 5 and not as low as -2. 

Notice that it is discontinuous at x=2.  It does not include the point where the
open circle is drawn but it "jumps" up to the point (2,1.5) where there is a
closed circle.  Notice that there are also points marked at (-1,1.5) and (4,1.5)
which shows that p(-1) = p(4) = 1.5.

So this graph meets all your requirements.

Edwin</pre>