VoW #2: Domain and Equation of a Line

VoW #2: Domain and Equation of a Line


Welcome to the second installment of the
video of the week. In this video of the week we’ll be talking about what you
should be doing right now. I’ll be giving you some notes about domain because
those can be pretty tricky problems and we’ll talk about how to find the
equation of the line between two points because students tended to struggle on
that problem on the final exam. So first off what should you be doing right now,
well you should be registered at MyMathLab.com as soon as possible. I
notice that most of the classes already done that so if you haven’t please do it
now and get started with the class. To do that, follow the instructions in the
email i sent you previously. Second you should be working on the chapter 1
homework assignment. When you log into the course itself you’ll notice that the
first page that comes up is right here if you want to work on the first
chapters homework assignment just click that link right there start working on
problems and let me know if you have any questions. Okay let’s talk about domain, so
two main things you want to know at this point in the course about domain.
Typically what you’ll be asked is to find the domain of some function and
you’ll be given some function. Two things you’re looking for, one you’re going to
have restriction on domain if you have a denominator in your function. More
specifically the denominator in your function cannot equal zero. If you had an
example say like G of X is 1 over X minus 2. That X minus 2 is your
denominator and we know that that cannot equal zero so X minus 2 cannot equal zero. Well if we add 2 to both sides of this thing we get that X cannot equal 2 and that is
the restriction on your domain, and all that means is you can’t plug X equals 2
into this function and get an answer because if you plug X equals 2 into this
function you get a zero in the denominator. Okay now if you want t communicate this I
deal with someone that X cannot be two in your denominator there’s two ways to
do it. There’s set notation and there’s interval notation. In this case set
notation is pretty simple it looks like this, these are sort of the curly
brackets on the outside and what this means is the set of all X values. The
vertical line means such that and then X is not equal to 2. So what this means is X could be any number other than X equals 2 and it
would be part of the domain of this function because you can plug any number
into this function except for x equals 2. Interval notation is just another way to
say the same exact thing and when I think of interval notation I think of an
actual interval. Draw it out here 01 and what I think is I can plug any X value I
want into that function except for X equals 2. So the domain of my function is
everything from negative infinity all the way up to 2 and then everything from
2 all the way out to infinity. I”m going to write out those two intervals
negative infinity to 2 and 2 all the way to infinity. Notice I’m not including
negative infinity and I’m not including two in my interval, and the way we combine these two intervals is with what we call a union. So this example that turn out to
be actually fairly long is asking you to find the domain of G of X which is this
function right here and there are two possible answers if you’re asked for set
notation this is your answer right here. If you’re asked for interval notation
that’s the answer right there. Okay so that’s one example another thing that
you want to know about domain in this chapter is that you can’t have a
negative under a square root. You’ve learned from some math class in the past
it if you have a negative number under a square root that it’s not a real number.
If I want to be a little bit more technical about this technically there
is a 2 here that’s why it’s a square root we don’t write it typically if
there was a 3 here would be called a cubed root and it doesn’t matter if
there are negatives under a cubed root, however if there was a 4 here you can’t
have a negative under a fourth root either. So the general rule to follow
here is that you can’t have a negative under an even root an even number root.
Cubed root in fifth root and 7 through those are all okay but if you have an
even number here you can’t have a negative number under that. So let me
give you an example real fast a common example would be something like this.
There’s a square root it’s an even root and you have something under it, well we
I think that can’t be negative. So that thing right there, has to be positive or
it could equal zero. We subtract 4 from both sides of this, we get that X
has to be greater than or equal to negative 4. What this means is I can plug
any X value into this function that I want as long as X is greater than or
equal to negative 4. Why, well if I pick the number that was less than negative 4 I
would get a negative under my square root and that’s not a real number, so
that X couldn’t be part of our domain. Okay let’s write this answer out in both
set notation and interval notation. Set notation is the same as before, it’s the
set of all X values such that X is greater than or equal to negative 4 and
that would be your answer if you’re asked for set notation. For interval
notation I always like to draw a little picture, if we draw out all of the numbers
on this interval that are greater than or equal to negative 4 we get something
like that. We only have one interval here as compared to the last example where we
have two intervals that were separated. So we’re answer in this case is just
negative 4 out to positive infinity, make sure that you include the negative 4 in
this example because of the equal sign. here. What that looks like an interval
notation is this right here, okay so let’s recap. If you’re asked the domain
question if you’re asked to find the domain of a function you’re looking for
two things denominators and even roots. If you see yourself with a denominator
you need to make sure that that denominator cannot be zero if you have
an even root in the problem you need to make sure that whatever is inside of
that even root has to be greater than or equal to zero. Okay I hope that helps with
that problem one more problem I’d like to talk a little bit about which is very
common in this class is finding the equation of a line between two points
I’ll make up an example. Let’s say we want to find the equation of a line
between those two points right there, well in order to find the equation of
any line we first need a slope and you have a formula for slope in your book.
Some people think of it as rise over run, it’s the difference between your Y
values divided by the difference between your X values.
Gives us that our slope in this example is a fraction and it’s negative 10 9ths.
Once you have the slope and a point, either point works, you can plug these
two things into point-slope form or slope intercept form to finish off the
equation of your line, I’ll show you the point-slope form way to do it. There’s
the point-slope formula right there what we’re going to do is take either point
that you’d like, I’ll choose the point negative 2 4 and we’re going to plug that
with our slope into this equation. You’ll notice that the Y itself and the X
variables have to stay in the equation we need those for the equation of a line
and then I’m going to do a little bit of algebra. I’m going to distribute the 10 9ths
through the parenthesis then we’re going to get Y by itself because typically
getting Y by itself is the form that we’d like our line to be in. Now the only
thing we have left to do is to combine the 29th with the four, so I’m going to
take a couple more lines to do this what we need to do is find a common
denominator between this four or we can think of it as four over one and the 29ths.
The way that we do this is we multiply this by nine over nine. That’s going to
convert the four into 36 ninths and now we’re allowed to combine these two
fractions together and we get the final answer for the equation of the line that
passes through the two points that I made up up here, that final equation is, Y
equals negative 10 9ths X + 69. Okay so hopefully that was a hard enough example
for you to get something out of it, just as a recap what you should be doing
right now is making sure that you’re registered for MyMathLab.com, and you should be working on that chapter on homework so that you can be sending me questions
and getting ready for that quiz that is due pretty soon. Hopefully you learned a
little something about domain in this video and hopefully um this example of
finding the equation of line between two points helped you out a bit. Let me know
if you have any questions and I’ll see you in the next video.

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