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Let's do
another one:
Graph
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2
things
and
2 sentences!
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The
y-intercept: Find
f(0)
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The
x-intercept:
numerator =
0, solve
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Vertical asymptotes:
denominator =
0, solve
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Horizontal asymptote:
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*When this is the case, we're
going to be forced to "quickie plot" a few points to nail the
graph. No, this is not being a sissy -- we'll have no
choice. Calculus will take care of this though!
OK, let's start graphing!
Let's get our
intercepts and
asymptotes down:
Since we've got that pesky
y =
0
horizontal asymptote, we can't use our "nowhere else" info on
the x-intercepts to figure out the "upstairs" or "downstairs" stuff.
Until we have Calculus, we're going to have to humble ourselves
and plot some points -- kind of! We're going to avoid
taking that pathetic trip to Sissyville by cheating a little
bit... I call it "quickie plotting."
Four strategically located
points will do it and all we really need to know is if he's
above or below the x-axis at each point.
We'll be plugging
x's into the
factored form:
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*We
only care about positives and negatives -- see if you
can do it! |
Now we've got it!
*Remember that he can only cross the x-axis at
x =
0... So, once
he's below, he'll be stuck there... and, once he's above,
he'll have to stay above! |
YOUR TURN:
| Graph |
 |
(You
already have all the pieces!) |
*Remember
that, when you are working these things out -- write out
all of your work in a neat and organized way! This
is one of the main reasons you have to take math classes
-- they teach you to organize your thoughts AND TO
THINK!
Continued on the
next
page
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The printing
and distribution and/or downloading of these lessons is strictly
prohibited. |
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