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Function notation example

Sal uses function notation to help Frank figure out how much water he can put in his balloon. Created by Sal Khan.

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  • blobby green style avatar for user Saba  Ali
    At don't you multiply each of the terms by three to get 4 as a whole number, not divide?
    (7 votes)
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  • leafers tree style avatar for user Adeola Boye
    why did he divide 27 by 3 at instead of 4 divided by 3?
    (11 votes)
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    • leaf blue style avatar for user Stefen
      You are free to do it in which ever order is easier for you (as long as you observe PEDMAS).
      In this example we have 3³=27 and 4/3.
      If you did 4/3 first, then you would have to work with 1.33333333333 (inaccurate), or the mixed fraction "1 and 1/3" and multiply those by 27.

      So now you have to multiply 27 by 1.33333333333 or "1 and 1/3" that to get the answer. Can you do that in your head?

      Sal noticed that 27 is divisible by 3, that is 3x9=27, and with that he can simplify the expression by removing a factor of 3 from the 3 in 4/3 and 27 to get 4 and 9 to get 36 - easy to do in your head.

      You also could have taken the factor of 3 out of 3³ and 4/3, to get 3² and 4 to get 9 and 4 to get 36 - also easy to do in your head.

      So you can do it in the order that is easiest for you - the goal is always to reduce careless errors.
      (17 votes)
  • aqualine ultimate style avatar for user amvasquez102
    besides just water balloons, where does function notation come in handy?
    (7 votes)
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    • piceratops ultimate style avatar for user moomoosnake
      Function notation in maths is analogous to the list of ingredients you get given in a recipe. It won't tell you how to make the cake but it will tell you what ingredients you'll need to get when you go shopping! It's used practically in physics, and is one of the key elements in computer programming. It's particularly useful when you're looking at messy relationships with multiple variables. as it provides a quick idea of which variables are important in determining something's value.
      (8 votes)
  • piceratops seed style avatar for user James Mugo
    How do you compute the area of a rectangle as a function of it's width given its perimeter.
    (5 votes)
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    • leaf grey style avatar for user Qeeko
      Let w denote the width and h the height of the rectangle in question. Given the perimeter P, we may write P = 2w + 2h. Hence h = P/2 - w. The area as a function of its width is then given by
      A(w) = wh = w(P/2 - w).
      (8 votes)
  • duskpin ultimate style avatar for user Nneka
    I'm not sure if I'm right...
    So since this is a function, would the radius be the input/domain?
    (8 votes)
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  • aqualine ultimate style avatar for user evelyn.lai
    hi, can someone help me with this problem I got? I don't know why my answer was wrong.
    f(x)=-x-4. find f(-4)
    the answer options were
    a.0 (this was the correct answer)
    b.-8 (this was the answer I got)
    c. 4
    d. 8
    (4 votes)
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    • mr pants green style avatar for user Savraj Sahota
      In this case, you would simply need to plug in -4 into the equation. So, f(-4)=-(-4)-4. This equals zero because you have a negative times -4, which equals positive 4. Then, you subtract 4, which equals 0! I think you forgot about the negative. Let me know if this helps!
      (6 votes)
  • piceratops ultimate style avatar for user Yusef Gadson
    I need help with evaluating functions
    (5 votes)
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  • starky ultimate style avatar for user Sannuth Rao
    Why do you not also multiply Pi in 4/3 Pi r cubed. When the answer of the question gets to 4/3 Pi 27, why do you not have to multiply Pi with 27 and 4/3 in the problem. Is the problem solving for Pi
    (4 votes)
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    • leafers ultimate style avatar for user ⓪_⓪
      Pi is an irrational number, and thus cannot be solved for all the way- It goes on forever without a pattern and cannot be represented as a fraction. The answer is impossible to get without rounding (inaccurate) or leaving the pi out. Thus, in order to avoid confusing the watcher by providing a non-simple or incorrect number, he chose not to multiply pi into the other values.
      (2 votes)
  • marcimus purple style avatar for user Viola
    At , why doesn't Sal solve 36(3.14)? Why does he leave it as 36Pi?
    (4 votes)
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  • duskpin sapling style avatar for user Liz
    Why did he randomly divide by 3 at ? What rule is that? Maybe I'm missing a subject/video where he went over these equations in more depth because he doesn't elaborate much here
    (2 votes)
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    • male robot donald style avatar for user Venkata
      He just simplified the expression. We have 27/3. How many times does 3 go into 27? From your tables, you know that 9 x 3 = 27. So, 27/3 = 9. This is the same idea he applied here. He cancelled 3 and got 1 (as 3 goes into 3 1 time) and cancelled 27 and got 9 (as 3 goes into 27 9 times)

      Alternatively, you can just divide the numerator and denominator by 3. You'll get (27/3)/(3/3). The numerator becomes 9 and denominator becomes 1. So, you get 9/1 = 9
      (3 votes)

Video transcript

Frank wants to fill up a spherical water balloon with as much water as possible. The balloons he bought can stretch to a radius of 3 inches-- not too big. If the volume of a sphere is-- and this is volume as a function of radius-- is equal to 4/3 pi r cubed, what volume of water in cubic inches can Frank put into the balloon? So this function definition is going-- if you give it a radius in inches, it's going to produce a volume in cubic inches. So let's rewrite it. Volume as a function of radius is equal to 4/3 pi r cubed. Now, they say the balloons he bought can stretch to a radius of 3 inches. So let's think about, if the radius gets to 3 inches, what the volume of that balloon is going to be. So we essentially would just input 3 inches into our function definition. So everywhere where we see an r, we would replace it with a 3. So we could write-- and just to be clear, let me rewrite it in the same color. V of-- that's not the same color. We do it in that brownish color right over here. So V of 3 is equal to 4/3 pi-- and instead of r cubed, I would write 3 cubed-- 4/3 pi 3 cubed. This is how the function definition works. Whatever we input here, it will replace the r in the expression. So V of 3 is going to be equal to-- so this is going to be equal to 4/3 pi times-- 3 to the third power is 27. 27 divided by 3 is 9, so this is 9. 9 times 4 is 36 pi. So this is equal to 36 pi. And since this was in inches, our volume is going to be in inches cubed or cubic inches. So that's the volume of water that Frank can put in the balloon-- 36 pi cubic inches.