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>> In this video,
we're going to look at
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evaluating a function
for a given value.
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I've got this function up here.
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F(x) = -4x^2-7x+9.
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The first thing that you really
want to make sure you're
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comfortable with is the
notation for functions.
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This, I read this
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f(x) the first time you
see function notation,
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it looks like f*x,
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where f is some variable and
x is some other variable.
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But that is totally not
what's happening here at all.
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What we have is f(x).
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We have a function f and
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it's going to be evaluated
at a variable x.
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In other words, we're going
to take x and plug it
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in to this equation over here.
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A lot of times when I'm
first teaching functions,
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I'll remind the students that
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f(x) is really the
same as y. I could
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rewrite this whole thing as
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y = -4x^2-7x+9 and it's
basically the same equation.
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This is function notation
up here in black
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and this is just written with
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two different
variables here in red,
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but it's the same exact thing.
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Let's say we want to evaluate
this function at 1/3.
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In function notation, I
would write it like this.
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I would say find f(1/3).
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What that means is plug
1/3 in for x up here.
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If I was doing it with the
equation in two variables,
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I would say find y when x = 1/3.
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If I gave you that
equation and told
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you to find y when x = 1/3,
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you just take 1/3 and plug
it in for all that stuff.
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If I give you this
function notation
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until you to find f(1/3),
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then you just plug 1/3 in
where all the x's are.
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I'm going to rewrite
this equation.
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Wherever there's an x,
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I'm going to put a 1/3.
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There's two spots
I need to put 1/3.
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Now from this point,
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it's just a matter of arithmetic
in order of operations.
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It's nothing fancy.
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It's just working
the problem out.
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As a reminder, let's write
our order of operations,
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parentheses or grouping symbols,
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exponents, multiplication,
division, those are equals.
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We do them left to right
and addition, subtraction.
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Those guys are equals. We
do them left to right.
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Addition does not always
come before subtraction
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and multiplication does not
always come before division,
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it depends which ones first.
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In this problem, it looks
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like we have some
parentheses here.
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A lot of people say,
well I have parentheses,
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but parentheses really means to
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simplify what's inside
the parentheses when
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we're talking about the order
of operations and this is
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already simplified
inside the parentheses.
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The parentheses in
this case are really
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just standing for
multiplication.
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The next thing we're going
to look at is exponent's.
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We do have an exponent
here, (1/3)^2.
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We're going to
bring down the -4.
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We're going to do (1/3)^2.
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Now I'm going to keep
these parentheses
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because in this case it
means multiplication.
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I still need to multiply
my answer by -4,
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1^2 is 1 and 3^2 is 9.
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That's as easy as it is
for squaring fractions.
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A lot of people think
that's tough. It's not.
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You just square the top,
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square the bottom, you're done.
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I'll bring the rest of this down
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and we'll go to the next step,
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which would be
multiplication or division.
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Don't have any division.
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Technically, a fraction is
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a division problem,
but if you divide it,
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you're going to
get a decimal and
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we're not putting
these in decimals,
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we're going to keep
it in a fraction.
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We're not going to
do that division,
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we're going to do
the multiplication.
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We're going to take -4*1/9.
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Some of you are
really good at this
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and already have the
answer in your head.
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Those of you out there that are
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still struggling with
fractions a little bit.
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Remember when you
multiply fractions,
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you just multiply the
numerators and denominators.
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If you have a whole number
like four, -4 is an integer.
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Positive four is a whole
number technically.
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But if you have a number that's
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not a fraction like an integer,
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like -4, that's
the same as -4/1.
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Sometimes it helps to
write that in there.
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Seven is the same as 7/1.
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Once you get used to that,
you don't have to write
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that over one stuff
because you can
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see it in your head that
you're going to multiply
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the -4*1 is -4,
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1*9 is 9.
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With the -4 or you can think of
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it out in front like -4/9.
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That's probably the best
way to think of it.
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At this point, is
-4/9. Over here.
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Then we're going to
bring down our -7/3+9.
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Well, at this point we need
to get a common denominator.
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Let's get a common
denominator of nine.
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You know what I'm going
to do? I'm going to
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do these two fractions first.
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A lot of times when you have
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just adding a whole
number at the end,
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you can do it in your head.
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Let's just do the fractions
and see what we've got.
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I'm going to multiply
this by 3/3 to
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change it to 1/9 and bring
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the -4/9 down, -7*3 is (21/9)+9.
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When you're adding or
subtracting fractions,
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you add or subtract the
numerators, -4-21 is (-25/9)+9.
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Now some of you guys might
want to change this nine to
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81/9 and get a
common denominator.
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That's fine. I'm going to
go ahead and finish it
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this way. Negative 25/9.
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Now I'm going to divide, I
have an improper fraction,
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so nine goes into 25,
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2 times, -2 and how
many are leftover?
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Let's see 18, so
that'd be seven.
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I've got this now,
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-2 (7/9)+9, which is really
the same as 9-2 7/9.
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That's the same thing.
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Nine takeaway 2 would be 7,
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take away 7/9 more
would be 6 2/9.
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If I lost you there,
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let me show you this other
way that you can do it.
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Let's go this way
with the blue arrow.
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I could keep the 25/9 and then
change the nine into 1/9,
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which would be 81/9, 81/9 is 9.
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Then do -25+81 on the top,
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which is the same as 81
takeaway 25, which is 56/9.
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Of course, 56/9 is
the same as 6 2/9.
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You could do it either
way with the fractions.
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Whichever way makes more sense
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to you is the way that
you should do it.
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But back to the main concept of
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evaluating a function
for a given value.
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It's just a matter of
plugging in whatever number
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is in there for x that's
going to go where the xs are.
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You going to put that
number in for x,
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whatever is in this parentheses
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that goes in where the xs are.
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Then just make sure you
follow your order of
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operations and watch
out for those things
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like positives and negatives and
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fractions and denominators
and stuff like that,
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then it becomes a
problem from your past.
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Hope that helps and makes
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functions a little
easier to understand.