2-7-59
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We're going to take the two to the left side and get a common
denominator of X + 3.
So once we get the common denominator and everything to
one side with zero on the other, we're going to distribute the -2
through.
So we get X -, 3 -, 2 X -6 combining our like terms
negative X - 9 / X + 3 less than or equal to 0.
So to get the vertical asymptotes we set the
denominator equal to 0.
To get the X intercept, we set the numerator equal to 0
horizontal asymptotes.
The degree on top and degree on bottom are the same, so it's
just the ratio of the leading coefficients.
To get the Y intercept, we set zero as X and we get zero -3.
So if we put all this information on a graph that
should look something like this, when we are way out at X going
to Infinity, we know we've got to be close to the horizontal
asymptote.
We've got to go through the Y intercept and get close to the
vertical asymptote.
This vertical asymptote here came from right here in the
denominator.
Its multiplicity is odd because it's all understood to the first
power.
So if the YS on one side are negative, the YS on the other
side are going to be the opposite or positive.
I've got to go to the X intercept.
The X intercept came from this numerator term and it's
understood to be to the first power.
So if the YS on one side are positive, the YS on the other
side are going to have to be negative.
We have to get closer and closer and closer to the asymptote as
we go out to negative Infinity.
Now we want where it's less than or equal to 0.
So we want all the Y values that are going to be less than or
equal to 0 or Y values that are negative.
So when we look at this graph, we're going to need negative
Infinity up to that intercept point of -9.
Because we wanted less than or equal to.
We're going to use a bracket there.
We're going to have union.
We need where else the YS are less than or equal to 0.
So from the vertical asymptote -3 out to positive Infinity,
we're going to use a parenthesis at -3 because it's an asymptote
and we can never cross a vertical asymptote.
So this is our answer.
If we look at our choices in Course Compass, we've got this
line with the bracket at -9 and then a parenthesis at -3 going
off to the right.