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Evaluate a Function at Given Values

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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.
Title:
Evaluate a Function at Given Values
Description:

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Video Language:
English
Duration:
07:39

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