Question 988860: 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
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713)   (Show Source):
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
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: 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 ≤ 5, p(-1)=p(4), and p is discontinuous at x=2.
This would be a piecewise function. Here is an equation of such a function:
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:
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 ≤ 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
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